A     TREATISE 


ON   THE 


PRINCIPLES    OF    CHEMISTRY. 


Eontion:    C.  J.  CLAY  AND  SON, 

CAMBRIDGE  UNIVERSITY  PRESS  WAREHOUSE, 

AVE  MARIA  LANE. 


:  DEIGHTON,  BELL,  AND  CO. 

Hetpjfg:   F.  A.  BROCKHAUS. 


A    TREATISE 


ON   THE 


PRINCIPLES  OF   CHEMISTRY 


BY 


M.  M.  PATTISON   MUIR,   M.A.,  F.R.S.E. 

l  I 

FELLOW,    AND   PR/ELECTOR  IN  CHEMISTRY  OF  GONVILLE  AND  CAIUS   COLLEGE, 

CAMBRIDGE. 


'In  nature  everything  is  distinct,  yet  nothing  defined  into  absolute 
independent  singleness."    WORDSWORTH. 


CAMBRIDGE  : 
AT    THE     UNIVERSITY     PRESS. 

1884 


If  in  this  book  I  have  shewn  any  just 
appreciation  of  the  scientific  study  of  nature, 
I  owe  it  to  the  teaching  of 

PROFESSOR   SIR   WILLIAM   THOMSON. 
To  him,  therefore,  I  dedicate  my  work. 


PREFACE, 


THIS  book  is  intended  to  give  a  fairly  complete  account 
of  the  present  state  of  knowledge  regarding  the  principles 
and  general  laws  of  chemistry. 

It  is  addressed  to  students  of  this  science  who  have 
already  a  considerable  acquaintance  with  descriptive  che- 
mistry, but  it  is  hoped  that  by  such  students  the  book  will 
be  found  complete  in  itself;  so  that  while  it  certainly  deals 
with  chemical  principles  and  theories  on  the  supposition  that 
its  readers  have  some  knowledge  of  chemical  facts,  yet  the 
book  may  fairly  claim  to  rank  as  a  systematic  treatise  on 
chemical  philosophy. 

While  I  have  tried  to  supply  full  information  regarding 
those  points  which  appear  to  me  of  most  importance,  I  have 
also  sought  to  avoid  great  detail,  and  to  present  a  sketch  of 
the  principles  of  chemistry  the  parts  of  which  shall  hang 
together  as  being  mutually  dependent. 

To  know  what  to  omit  has  been  one  of  the  most  difficult 
parts  of  my  undertaking.  The  chemical  student  is  too  often 
subjected  to  a  shower-bath  of  facts;  he  is  made  to  feel  that 


Vlll  PREFACE. 

'  to  sit  as  a  passive  bucket  and  be  pumped  into... can  in  the 
long-run  be  exhilarating  to  no  creature.' 

An  attempt  is  made  in  this  book  to  treat  the  principal 
theories  of  modern  chemistry  to  some  extent  from  an  his- 
torical point  of  view,  and  to  trace  the  connections  between 
the  older  theories  and  those  which  now  prevail  in  the  science. 
It  is  hoped  that  the  student  may  thus  gain  a  firmer  grasp  of 
those  theories  than  he  is  able  to  do  when  they  are  put  before 
him  as  entirely  creations  of  recent  times. 

I  have  tried  to  deal  with  chemical  facts  and  generalisa- 
tions so  as  to  shew  their  reality.  This  can  best  be  done, 
I  believe,  by  following  in  the  very  foot-prints  of  the  great 
discoverers,  by  watching  them  as  they  make  their  footing 
sure,  and  as  they  feel  their  way  up  the  heights.  That  the 
student  may  be  able  to  verify  the  accounts  I  have  given  of 
the  more  important  investigations,  and  more  especially  that 
he  may  fill  in  the  details  which  I  have  necessarily  omitted, 
I  have  given  copious  references  to  original  memoirs  and 
papers ;  these  references  will,  I  believe,  be  found  correct,  at 
least  I  have  spared  no  pains  to  make  them  so.  I  have  also 
endeavoured  to  make  the  index  full  and  complete. 

So  far  as  I  am  aware,  no  sufficiently  comprehensive  guide 
to  the  study  of  the  principles  of  chemistry  exists,  in  an 
English  form,  although  we  have  many  excellent  works  dealing 
with  descriptive  chemistry,  with  the  materials,  that  is  to  say, 
from  which  chemical  science  is  being  constructed.  Professor 
Lothar,  Meyer's  Die  Modernen  Theorien  der  Chemie,  to  a 
considerable  extent  meets  the  wants  of  the  German  student. 
I  have  made  free  use  of  that  book  in  preparing  my  own ;  but 
I  venture  to  think  I  have  incorporated  in  my  general  plan 
many  important  facts  and  principles  which  do  not  find  a 


PREFACE.  IX 

place  in  that  admirable  treatise.  I  have  also  regarded  the 
whole  subject  from  a  stand-point  somewhat  different  from 
that  occupied  by  the  German  Professor. 

To  name  all  the  books  and  journals  from  which  I  have 
derived  assistance  would  be  tedious  and  absurd;  they  are 
sufficiently  indicated  in  the  notes  and  references1. 

I  have  tried  to  rest  every  important  statement  on  first- 
hand authority.  When  chemistry  is  regarded  from  the  point 
of  view  of  the  great  workers  therein,  it  wears  an  aspect 
very  different  from  that  with  which  it  confronts  the  mere 
text-book-taster. 

The  book  is  divided  into  two  parts.  The  first  part  is 
occupied  with  the  statement  and  discussion  of  the  atomic  and 
molecular  theory,  and  the  applications  thereof  to  such  sub- 
jects as  allotropy,  isomerism,  and  the  classification  of  elements 
and  compounds.  Somewhat  full  accounts  are  also  given,  in 
this  part,  of  thermal,  optical,  and  other  departments  of  physi- 
cal chemistry,  in  so  far  as  the  results  and  methods  of  these 
branches  of  the  science  are  applicable  to  the  questions  re- 
garding the  composition  of  chemical  systems  which  are 
connoted  by  the  term  Chemical  Statics. 

The  second  part  of  the  book  is  devoted  to  the  subjects  of 
dissociation,  chemical  change  and  equilibrium,  chemical 
affinity,  and  the  relations  between  chemical  action  and  the 
distribution  of  the  energy  of  the  changing  system.  These, 
and  cognate  questions,  I  have  ventured  to  summarise  in  the 
expression  Chemical  Kinetics. 

I  have  been  much  aided  in  my  task  by  my  friends 
Mr  C.  Slater,  B.A.,  of  St  John's  College,  and  Mr  R.  Threlfall, 

1  The  full  titles  of  the  various  journals  referred  to  are  given  on  pp.  xxi,  xxii. 
M.  C.  b 


X  PREFACE. 

B.A.,  Scholar  of  Gonville  and  Caius  College.  The  former 
has  read  considerable  portions  of  the  proofs  and  has  made 
many  valuable  suggestions  ;  the  latter  has  read  all,  except 
the  first  chapter  of  Book  I,  and  by  his  criticisms  and  remarks 
has  helped  me  to  make  many  important  points  much  clearer 
and  more  accurate  than  they  would  otherwise  have  been. 

M.   M.   PATTISON    MUIR. 

/ 
CAMBRIDGE,  October  1884. 


TABLE  OF  CONTENTS. 


BOOK   I.      CHEMICAL    STATICS. 


CHAPTER  I.  ATOMS  AND  MOLECULES. 

Paragraph  Page 

INTRODUCTORY i 

Beginnings  of  atomic  theory i  7 

Daltonian  conception  of  atoms 2,3  8 

Volumetric  combinations  of  elementary  gases 


Law  of  Gay-Lussac 

Dalton's  criticism  of  this  law 5  12 

Avogadro's  generalisation 6  13 

Wollaston's  equivalents 7  14 

Berzelius's  work  on  atomic  synthesis 8  16 

The  Berzelian  double  atom 9  19 

Dumas's  attempts  to  determine  molecular  and  atomic  weights       .  10  20 

Notation,  and  system  of  Laurent  and  Gerhardt     .         .         .         .  n  21 

The  atom,  the  molecule,  and  the  equivalent  differentiated      .         .  12  24 

The  molecular  theory  of  the  constitution  of  matter         ...  13  24 
Application  of  Avogadro's  law  to  determine  relative  weights  of 

elementary  molecules 14  29 

Table  of  molecular  weights  of  elements 15  31 

Precautions  to  be  observed  in  determining  molecular  weights         .  16  32 

Correction  of  values  obtained 17  34 

Deduction,  from  application  of  Avogadro's  law,  of  definition  of 

atomic  weight 18  35 

Table  of  data  for  finding  maximum  atomic  weights  of  elements     .  19  36 

Atomicity  of  elementary  molecules 20  42 

Formulae  of  liquid  and  solid  compounds 21  43 

Table  of  maximum  atomic  weights  of  elements      ....  22  44 

Law  of  Dulong  and  Petit 23  45 

Application  of  this  law,  in  modified  form,  to  compounds       .         .  24  46 

Data  concerning  atomic  heats  of  elements 25  48 

Indirect  determination  of  atomic  heats  .  ...  26  51 

Discussion  of  law  of  Dulong  and  Petit  .         .     .    .         .         .27  56 

b2 


Xll  TABLE  OF   CONTENTS. 

Paragraph  Page 

Specific  heat  of  beryllium 28  58 

,,  boron,  silicon  and  carbon 29  59 

Limitations  to  application  of  law  of  Dulong  and  Petit  .  .  30  62 
Comparison  of  law  of  Avogadro  with  that  of  Dulong  and  Petit  as 

aids  in  finding  values  of  atomic  weights  ....  31  63 

Mitscherlich's  law  of  isomorphism 32  65 

Groups  of  isomorphous  elements 33  67 

Di-,  tri-  and  poly-  morphism 34  69 

Application  of  this  law  to  determine  values  of  atomic  weights  .  35  69 

Chemical  methods  for  finding  molecular  and  atomic  weights  .  .  36  71 
Comparison  of  chemical  with  physical  methods  for  determining 

these  constants 37  77 

Table  of  atomic  weights,  with  summary  of  data  (and  references  to 

original  memoirs) 38  77 


CHAPTER  II.     ATOMIC  AND  MOLECULAR  SYSTEMS. 
SECTION  I.     NASCENT  ACTIONS. 

Examples  of  actions  called  nascent 39  78 

Explanation  of  these  actions  in  terms  of  the  molecular  theory  .  40  89 

Nascent  state  of  compounds 41  90 

Special  cases :  action  of  acids  on  metals 42  92 

Experimental  evidence  of  difference  between  actions  of  atoms  and 

molecules 43  97 

All  reacting  bodies  in  a  chemical  change  influence  that  change  .  44  102 
Should  the  expression  '  nascent  action '  be  retained  in  chemical 

nomenclature? 45  105 

SECTION  II.    THE  DUALISTIC  AND  UNITARY  THEORIES. 

Electro-chemical  investigations  of  Davy 46  106 

,,                    ,,                  Berzelius  .....  47  107 

The  Berzelian  dualistic  theory 48  no 

Dualistic  conception  of  acid  and  salt 49  1 1 1 

Faraday's  electrolytic  laws 50  112 

Reaction  against  dualism  led  by  Dumas,  Laurent  and  Gerhardt    .  51  112 

Conception  of  compound  radicle  retained  by  the  new  School         .  52  114 

Classification  by  use  of  typical  substances 53  115 

SECTION  III.    EQUIVALENCY  OF  ATOMS. 

Conception  of  definite  substituting  value  applied  to  atoms  .  .  54  117 
Fundamental  data  for  determining  precise  meaning  of  terms 

monovalent,  divalent,  &c 55  119 

Application  of  these  terms  to  classification  of  atoms  of  elements    .  56  120 


TABLE   OF   CONTENTS.  xiii 

Paragraph  Page 

Further  explanation  of  expression  valency  of  an  atom  .  .  .  57  122 
Deduction  (from  data)  of  values  to  be  assigned  to  this  constant  for 

different  elements 58  123 

Consideration  of  possible  meanings  of  expression  '•bonds'1  or  'units 

of  affinity^  as  applied  to  atoms 59  124 

Lossen's  use  of  terms  monovalent,  divalent,  £c 60  126 

Saturated  and  unsaturated  molecules 61  129 

Lossen's  definitions  of  these  terms 62  130 

General  considerations  regarding  valencies  of  atoms,  especially  as 

these  are  supposed  to  be  deduced  from  study  of  non-gasifiable 

compounds    .         .         •         •         •         •         •         •         •         •  63         131 


SECTION  IV.     ALLOTROPY  AND  ISOMERISM. 

The  molecule  considered  as  a  structure 64         133 

Differences  of  atomic  arrangements  are  connected  with  differences 

in  energies  of  molecules 65         134 

Two  kinds  of  variations  in  atomic  arrangement  possible         .         .  66         134 

Allotropy 67         136 

Polymerism  ..........  68         138 

Isomeric  and  metameric  molecules 69         138 

Formula  for  rinding  maximum  number  of  monovalent  atoms  in  a 

molecule 70         139 

Possible  isomerides  of  same  empirical  formula        .         .         .         .  71         140 

Formulae  of  molecules  which  cannot  exhibit  isomerism  .         .  72         141 

Illustrations  of  determinations  of  structural  formulae      ...  73         141 

Atomic  groups  characteristic  of  classes  of  carbon  compounds         .  74         146 

Recapitulation  of  paragraphs  concerning  applications  of  theory  of 

valency 75         150 

Generalisations  used  as  guides  in  finding  structural  formulas  .  76         151 

Illustrations  of  use  of  these  generalisations 77         151 

Further  application  of  theory  of  valency  to  conception  of  the 

molecule  as  a  structure 78         157 

Functions  of  parts  of  a  molecule  are  dependent  on  nature  and  struc- 
ture of  the  whole  molecule 79         157 

Illustrations  of  dependence  of  functions  of  parts  of  a  molecule  on 
the  nature  and  arrangement,  relatively  to  given  parts,  of  other 

atoms  in  the  molecule 80         158 

Illustrations  of  influence  exerted  on  the  function  of  one  atom,  or 
group  of  atoms,  by  the  arrangement  of  all  the  atoms  in  the 

molecule 81         162 

Chemical  stability  of  a  molecule  is  the  result  of  balance  between 

functions  of  various  parts  of  the  molecule       ....  82         169 

Many  physical  properties  of  compounds  are  also  correlated  with 

such  molecular  balance 83         170 

Thomsen's  thermal  investigation  of  the  '  dynamical  values  of  the 

carbon  bonds' 84         172 


xiv  TABLE   OF   CONTENTS. 

Paragraph     Page 

Bearing  of  this  investigation  on  existence  of  connection  between 

molecular  structure  and  molecular  energy       .         .         .         .  85         175 

Further  illustrations  of  this  connection 86         1 75 

Illustrations  of  existence   of   relations  between   greater   or  less 
molecular  energy  and 

(1)  the  actual  valencies  of  the  atoms  in  the  molecules  con- 

sidered           87         177 

(2)  the  distribution  of  reactions  between  the  atoms  in  the 

molecules 88         177 

General  considerations  regarding  relations  illustrated  in  pars.  87 

and  88 89         178 

Application  of  these  considerations  to  prevalent  views  on  valency  90         1 80 

Apparent  exceptions  to  that  explanation  of  isomerism  which  is 

based  on  the  theory  of  valency 91          1 8 1 

Properties  of  liquid  and  solid  compounds  are  to  some  extent  con- 
ditioned by  mutual  molecular  actions      .         .         .         .         .  92         183 

/  Physical  isomerism 93         185 

Work  of  Lehmann  on  this  subject 94         186 

Criticism  of  Lehmann's  division  of  physical  isomerides  into  phy- 
sical metamerides  and  polymerides 95         187 

Summary  of  section  IV. 96         191 

Appendix  to  section  IV. 

Lossen's  criticism  of  the  various  meanings  assigned  to  term 

valency '97         T94 

1  Are  the  carbon  bonds  of 'equal  value  £ " 98         199 

SECTION  V.     MOLECULAR  COMPOUNDS. 

Theory  of  valency  not  strictly  applicable  to  phenomena  suggested 

by  terms  molecular  compounds  and  atomic  compounds  .  .  99  202 

Definition  of  molecular  compounds  impossible  .  .  .  .  100  202 
Illustrations  of  phenomena  exhibited  by  gases  classed  as  molecular 

compounds 101  203 

Phenomena  exhibited  by  liquid  and  solid  compounds  belonging  to 

this  class 102  209 

Study  of  such  phenomena  leads  to  considerations  belonging  to 

chemical  kinetics 103         219 


CHAPTER  III.     THE   PERIODIC   LAW. 

Earlier  investigations  into  connections  between  atomic  weights 

and  properties  of  elements 104  223 

Statement  of  the  periodic  law 105  224 

Illustrations  of  periodic  connection  between  atomic  weights  and 

properties  of  elements  . 106  226 

Relations  between  atomic  weights  and  atomic  volumes          .         .  107  226 


TABLE   OF   CONTENTS.  XV 

Paragraph  Page 

Relations  between  atomic  weights  and  fusibility  of  elements  .  .  108  228 
,,  ,,  ,,  and  various  physical  constants 

of  elements    ..........  109         229 

Illustrations  of  applications  of  periodic  law  : 

(r)  to  predict  properties  of  unknown  elements        .         .         .  no         230 

(2)  to  guide  the  study  of  properties  of  similar  elements  .  in  233 

*  Odd  torus*  i  ( even  series',  '  long  periods •',  and  ' typical  elements'1  .  112  239 
Connections  between  general  formulae  of  classes  of  compounds  and 

atomic  weights  of  elements  in  these  compounds  .  .  .  113  242 
Forms  of  highest  oxides  considered  as  periodic  functions  of  atomic 

weights  of  the  elements 114  243 

Valency  considered  as  a  periodic  function  of  atomic  weights  of  the 

elements 115         245 


CHAPTER  IV.     APPLICATION  OF  PHYSICAL  METHODS 
TO   PROBLEMS   OF   CHEMICAL   STATICS. 

Introductory 116  249 

SECTION  I.    THERMAL  METHODS. 

Introductory 117  250 

Notation  used  in  thermal  chemistry 118  251 

Endothermic  and  exothermic  reactions           .         .         .         .         .  119  254 

Calculation  of  thermal  values  of  chemical  changes          .         .         .  120  257 
Illustrations  of  connection  between  chemical  changes  and  changes 

of  energy 121  265 

A  chemical  change  consists  of  at  least  two  parts    .         .         .         .  122  268 

Attempts  to  determine  thermal  values  of  molecular  decompositions  123  269 
Thermal  results  applied : 

(1)  to  nascent  actions 124  270 

(2)  to  allotropy 125  273 

(3)  to  classification  of  elements       ......  126  274 

(4)  to  classification  of  compounds           .....  127  275 

(5)  to  neutralisation  of  acids  by  bases,  and  of  bases  by  acids  .  128  279 
Influence  of  physical  conditions,  especially  temperature,  on  ther- 
mal value  assigned  to  a  chemical  change         ....  129  287 

Examples  to  shew  importance  of  considering  such  influence  .         .  130  292 
Influence  of  mass  of  reacting  bodies  on  thermal  value  of  a  chemical 

change 131  294 

Thermal  value  of  a  chemical  reaction  is  the  sum  of  several  partial 

values 132  295 

The  law  of  maximum  work 133  297 

Illustrations  of  application  of  thermal  methods  to  determine  struc- 
tural formulae          .         .      - 134  300 

Connections  bet  ween  boiling  points  and  composition  of  hydrocarbons  135  304 

Concluding  remarks  to  this  section 136  306 


XVI  TABLE   OF   CONTENTS. 

SECTION  II.    OPTICAL  METHODS. 

Paragraph    Page 

Statement  of  methods  to  be  considered  in  this  section  .         .         137         306 

Formulae  for  calculating  the  refraction-equivalent  of  a  carbon 

compound 138  306 

Is  the  value  to  be  assigned  to  the  refraction-equivalent  of  an  ele- 
ment constant  in  all  liquid  compounds  of  that  element?  .  139  309 

Is  there  any  connection  between  the  nature  of  the  atoms  directly 
bound  to  a  given  atom  and  the  refraction-equivalent  of  that 
atom? 140  312 

Meaning  to  be  assigned  to  the  expression  'refraction-equivalent  of 

an  atom' 141  316 

Connection  between  the  refraction-equivalent  and  the  actual  va- 
lency of  the  atom  of  carbon  .  .  .  .  .  .  142  317 

Application  of  refraction-equivalents  to  questions  regarding  struc- 
tural formulae 143  318 

Specific  rotatory  power  of  substances  .         .         .         .         .         .          144         318 

This  constant  depends  on  atomic  composition  of  molecules,  but 
is  also  modified  by  reactions  between  optically  active  and 
inactive  molecules 145  322 

van't  Hoff 's  hypothesis  regarding  connections  between  molecular 

structure  and  specific  rotatory  power  .....  146  323 

Illustrations  of  modifying  influence  exerted  by  optically  inactive 

substances  on  rotatory  power  of  optically  active  compounds  .  147  328 

Connections  between  absorption-spectra  and  structure  of  molecules 

of  carbon  compounds 148  331 

Summary  of  section 149         333 

SECTION  III.    METHODS  BASED  ON  VALUES  ASSIGNED  TO  THE 

CONSTANT,  ^5^i!l^. 
'  specific-gravity 

Explanation  of  constant  considered  in  this  section         .         .         .  150  334 
Data  to  illustrate  connections  between  this  constant  and  composi- 
tion of  compounds         151  325 

Data  to  illustrate  connections  between  this  constant  and  actual 

valencies  of  atoms  in  given  molecules    .         .         .         .  152  337 
Data  to  illustrate  connections  between  this  constant  and  distribu- 
tion of  interatomic  actions     153 — 4  338 

Values  of  this  constant  for  solid  compounds           ....  155  342 

Discussion  of  meaning  of  constant  in  question       .         .         .         .  156  345 

SECTION  IV.    METHOD  BASED  ON  '  ETHERIFICATION- VALUES'. 

Statement  of  method  .         .         .         .         .         .         ..         .         157         348 

Illustrations  of  application  of  this  method 158         349 

Concluding  remarks  to  Book  1 159        352 


TABLE   OF   CONTENTS.  xvil 


BOOK    II.     CHEMICAL   KINETICS. 


CHAPTER   I.     DISSOCIATION. 

Paragraph    Page 

Introductory  remarks  on  subject  of  this  book                                              160  353 
References  to  nascent  actions  and  to  molecular  compounds  as  sub- 
jects which  require  kinetical  treatment  .....   161 — 2  353 — 4 

Dissociation  contrasted  with  decomposition           ....         163  355 

Relation  between  dissociation  and  pressure  of  gaseous  products     .         164  356 

Dissociation  of  calcium  carbonate          ......         165  357 

Dissociation  is  a  reversible  process 166  357 

Dissociation  of  various  solid  compounds  into  solid  and  gaseous 

products 167  358 

Pfaundler's  hypothesis  to  account  for  facts  mentioned  in  last  para- 
graph   .168  360 

Summary  of  characteristics  of  dissociation-processes      .         .         .         169  361 
Illustrations  of  bearing  of  dissociation  on  determinations  of  vapour 

densities       ..........         170  362 

Changes  which  present  analogies  with  dissociation        .         .         .         171  366 

So-called  dissociation  of  salts  in  solution 172  367 


CHAPTER  II.     CHEMICAL  CHANGE. 
SECTION  I.    GENERAL  CONSIDERATIONS. 

Views  of  Berthollet  on  chemical  change  .  .  .  .  .  173  369 

Davy's  view  of  same  subject  .  .  .  .  .  .  .  174  372 

View  of  Berzelius  on  same  subject 175  373 

Reference  to  work  of  Guldberg  and  Waage  on  this  subject  .  .  176  373 
Rough  classification  of  miscellaneous  facts  regarding  chemical 

change 177  374 

'Contact-actions^  .  .  .  .  .  .  .  .  178  374 

' Predisposing  affinity '' 179  376 

'Induction' 180  378 

4  Influence  of  mass' 181  38: 

Sketch  of  the  theory  of  '  ctimulative  resolution"1  proposed  by  Mills  182  383 
Existence  of  some  compounds  only  as  members  of  a  system  from 

which  they  cannot  be  obtained  in  a  separate  state  .  .  .  183  384 
Application  of  knowledge  gained  in  this  section  to  conception  of 

molecular  structure        .         .         .         .         ...         .         .  184  385 


XV111  TABLE   OF   CONTENTS. 


SECTION  II.    CHEMICAL  EQUILIBRIUM. 

Paragraph  Page 

Methods  used  for  attacking  questions  of  chemical  equilibrium  .  185  386 

Williamson's  hypothesis 186  387 

Hypothesis  of  Pfaundler 187  387 

References  to  some  applications  of  Pfaundler's  views  .  .  .  188  391 

This  hypothesis  throws  light  on  subject  of  nascent  actions  .  .  189  391 

Also  on  contact-actions  and  predisposing  affinity  ....  190  392 

Hicks's  treatment  of  dissociation  as  a  special  case  of  equilibrium  .  191  393 

Reference  to  Horstmann's  thermodynamical  theory  of  dissociation  192  393 

Willard  Gibbs's  thermodynamical  treatment  of  equilibrium  .  .  193  394 
Foregoing  paragraphs  shew  importance  of  obtaining  measurements 

of  speed  of  chemical  changes 194  398 

Gladstone's  work  on  this  subject  .......  195  398 

Work  of  Harcourt  and  Esson  on  the  same  subject  .  .  .  196  399 

Menschutkin's  determinations  of  velocity  of  etherification  .  .  197  399 
References  to  Kajander's  measurements  of  velocity  of  action  of 

acids  on  magnesium .  198  400 

Concluding  remarks  on  results  obtained  in  paragraphs  195 — 198  .  199  400 


CHAPTER  III.     CHEMICAL  AFFINITY. 

Historical  sketch  of  the  subject 200  401 

Berthollet's  theory 201  403 

Classification  of  the  methods  for  attacking  the  subject  .         .         .  202  405 


SECTION  I.    THEORY  OF  GULDBERG  AND  WAAGE. 

General  statement  of  the  theory 203  407 

Detailed  examination  of  the  expression  'coefficient  of  affinity  '         .  204  409 

The  expression  ^  coefficient  of  velocity'   ......  205  411 

Two  ways  by  which  the  theory  may  be  tested       ....  206  41  r 

Applications  of  the  theory    . 207  4^ 

,,  ,,  to  gaseous  systems       ....  208  4 14 

„  ,,  to  cases  of  dissociatioa         .         .         .  209  415 

Recapitulation  of  general  results  obtained  by  Guldberg  and  Waage  210  416 
Sketch  of  analytical  methods  employed  in  measuring  amounts  of 

chemical  change 211  416 

Ostwald's  development  of  the  theory  to  determine   relative  af- 
finities of  acids      212  417 

Examples  of  Ostwald's  method  of  procedure         .         .         .         .  213  419 

Relative  affinities  of  HC1,  H2SO4,  and  HNO3      .         .         .         .  214  420 


TABLE   OF   CONTENTS.  Xl'x 

Paragraph    Page 

Influence  of  nature  of  base  on  relative  affinities  of  acids          .         .  215  421 

,,          temperature               ,,                 ,,                                     .  216  422 

Further  illustrations  of  Ostwald's  volumetric  methods  .         .         .  217  422 

Examples  of  calculation  of  relative  affinities           .         .         .         .  218  423 

Chemical  methods  employed  by  Ostwald 219  424 

Action  of  acids  on  solid  calcium  oxalate 220  425 

Determinations  of  velocities  of  chemical  changes  may  be  employed 

to  determine  relative  affinities        ......  221  427 

Ostwald's  examination  of  the  action  of  acids  in  accelerating  the 

decomposition  of  acetamide  by  water    .....  222  427 

Analysis  of  the  coefficients  of  affinity  of  reactions  between  acids 

and  bases 223  429 

Ostwald's  study  of  the  influence  of  acids  on  the  decomposition  of 

methylic  acetate  by  water      .......  224 — 5  430 — i 

Ostwald's  study  of  the  influence  of  acids  on  the  inversion  of  sugar 

solutions 226  431 

The  affinity-constants  of  the  acids 227  432 

Thermochemical  methods  may  be  applied  to  determine  the  rela- 
tive affinities  of  acids    .         .         .         .         .         .         .         .  228  433 

Principles  on  which  Thomsen's  method  is  based  .         .         .         .  229  433 

Example  of  application  of  Thomsen's  method       ....  230 — 2  434 

Thomsen's  general  conclusion  regarding  the  '  avidities'1  of  sulphuric 

and  nitric  acids 233  437 

Thomsen's  general  conclusion  regarding  the  avidities  of  hydro- 
chloric and  nitric  acids 234  437 

Tables  giving   the   relative   affinities  of  acids  as  determined  by 

Ostwald  by  different  methods,  and  also  by  Thomsen      .         .  235  438 

The  specific  affinity-constants  of  the  acids  and  bases     .         .         .  236  441 

Concluding  remarks  on  Ostwald's  work 237  442 


SECTION  II.    THERMAL  AND  OTHER  METHODS  OF  STUDYING 
AFFINITY. 

General  remarks 238         443 

Difficulty  of  rinding  thermal  values  of  purely  chemical  changes  .  239,  240  443 
Thermal  method  of  measuring  affinity  is  founded  on  an  improbable 

hypothesis 241,  242  445 

Helmholtz's  researches  on  '  free '  and  '  bound '  energy  .  .  243  446 
Thermal  methods  may  give  measurements  of  differences  between 

coefficients  of  affinity  of  analogous  reactions  .  .  .  .  244,245  448 

Theory  of  vortex  atoms  may  throw  light  on  subject  of  affinity  .  246  450 
Joule's  electrical  theory  regarding  the  origin  of  the  heat  evolved 

during  chemical  changes        .                   247         451 

£» 

Sir  W.  Thomson's  formula  Q—  —                .         .         .         .         .  248         453 

Wright's  measurement  of  '  affinity  in  terms  of  electromotive  force'  249         453 


XX  TABLE  OF   CONTENTS. 

Paragraph  Page 
Helmholtz's  researches  on  the  connections  between  chemical  and 

electrical  forces 250  455 

Views  of  Helmholtz  compared  with  those  of  Berzelius  .  .  -251  458 
Pfaundler's  hypothesis  regarding  equilibrium  is  in  keeping  with 

Helmholtz's  electrical  theory  .  .  .  .  .  252  458 

Concluding  remarks  on  this  section  ......  253  458 


CHAPTER  IV.     OTHER  APPLICATIONS  OF  KINETICAL 

METHODS. 

Molecular  phenomena  of  gases  contrasted  with  those  of  liquids 

and  solids 254  462 

Formuloe  of  liquid  and  solid  compounds 255  465 

Kinetical  aspects  of  structural  formulae 256  466 

Structural  formulae  considered  in  the  light  of  Ostwald's  researches 

on  affinity 257  468 

Bearing  of  the  work  on  specific  volumes  and  refraction-equivalents 

on  this  question 258  470 

Ostwald's  work  establishes  a  connection  between  affinity  and 

molecular  structure       ........         259         472 

CONCLUDING  REMARKS 473 


TITLES   OF  JOURNALS   CONTAINING   MEMOIRS   TO 
WHICH   REFERENCES   ARE   MADE. 


ABBREVIATED  TITLES. 

Phil.  Trans. 
Prof.  R.  S. 
C.  S.  Journal. 


Phil.  Mag. 

Chem.  News* 

Nature. 

Brit.  Ass.  Reports. 

Proc.  R.  I. 

Anier.  Chem.  Journal. 

!Amer.  Journ.ofSci.  and^ 
Arts  \ 

Sill.  Amer.  Journal.     } 

Proc.  Amer.  A  cad.  of  Arts 

and  Sci. 
Gilberts  Ann. 


f.  Ann. 
Wied.  Ann. 

Pogg.  Beiblatter. 


FULL  TITLES. 

Philosophical  Transactions. 

Proceedings  of  the  Royal  Society. 

Journal  of  the  Chemical  Society . 

[Memoirs  and  Proceedings,  3  vols.  (1841-1847). 
Journal,  series  1,  15  vols.  (1848-186-2). 
„     series  2,  15  vols.  (1863-1877). 
„     Transactions    and    Abstracts    paged 
separately,   from    1878  to  present  time.     The 
volumes  of  this  Journal  are  sometimes  referred 
to  by  numbers  beginning  with  volume  i  of  series 
i,  and  running  on  consecutively  to  the  present 
time.] 

Philosophical  Magazine.     [Series  1  to  5.] 

The  Chemical  News.     [Beginning  from  1860.] 

Nature.     [1879,  anc^  onwards.} 

Reports  of  the  British  Association  for  the  Advance- 
ment of  Science.  [1831,  and  onwards.] 

Proceedings  of  the  Royal  Institution  of  Great 
Britain.  [1851,  and  onwards.] 

American  Chemical  Journal.  [1879,  and  onwards.] 

American  Journal  of  Science  and  Arts  ;  since  1880 
the  title  is  American  Journal  of  Science.  [Con- 
.ducted  by  Sillimann,  and  subsequently  by  Silli- 
mann  and  Dana.  Series  1  to  3.] 

Proceedings  of  the  American  Academy  oj  Arts  and 
Sciences.  [Series  1  and  2.] 

Gilbert's  Annalen  der  Physik  und  Chemie.  [1799- 
1824.] 

Poggendorff"1  s  Annalen  der  Physik  und  Chemie. 
[1824-1876.] 

Wiedemanrfs  Annalen  der  Physik  und  Chemie. 
[Continuation  of  Pogg.  Ann.  from  1877;  fre- 
quently quoted  in  memoirs,  &c.,  as  Ann.  Phys. 
Chem.  Series  2.] 

Beiblatter  zu  den  Annalen  der  Physik  und  Chemie. 
[1877,  onwards.] 


XX11 


TITLES   OF   JOURNALS   OF   REFERENCE. 


ABBREVIATED  TITLES. 
Annalen. 

J.filrprakt.  Chemie. 
Ber. 


^Fresenius* s  Zeitschr. 
\Zeitschr.  anal.  Chemie 
Zeitschr.  filr  Chemie. 


Zeitschr.  filr  Krystallog. 
Schweigger 's  Journal. 
Sitzber.  der  K.  Akad.  zu  Wien. 


Sitzber.  der  Wiss.  Akad.  zu 

Berlin. 
Jahresberichte. 


Compt.  rend. 
Mem.  de  FAcad. 

Ann.  Chim.  Phys. 
Butt.  Soc.  Chim. 

Mem.  de  la  Soc.  d'Arcueil. 

Mem.   couronn.    de   rAcad. 
Brux. 

Ann.  Min. 


FULL  TITLES. 

Liebig's   Annalen   der    Chemie    nnd    Pharmacie. 

[Continued  since  Liebig's  death  under  same  title.] 
Journal  filr  praktische  Chemie.  [Series  1  and  2.] 
Berichte  der  Deutschen  Chemischen  Gesellschaft. 

[Abstracts   of  papers   published  elsewhere  are 

paged  consecutively  with  the  transactions  until 

1883  ;   from   1884  and  onwards  the  abstracts, 

Eeferate,  are  paged  separately.] 
Zeitschrift  fur  analytische  Chemie,  herausgegeben 

von  Dr  C.  R.  Fresenius.     [1862,  onwards.] 
Zeitschrift  filr  Chemie.     [Conducted  by  Beilstein 

and   Fittig.     Series  1  and  2.     1858  to  1871. 

Publication  discontinued.] 
Zeitschrift  filr  Krystallographie  und  Mineralogie. 

[1877,  onwards.] 
Journal  filr  Chemie  ^tnd  Physik.     [Conducted  by 

J.  S.  C.  Schweigger.     1811-1833.] 
Sitzungsberichte    der    Mathematisch-natiirwissen- 

schaftliche  Class e  der  Kaiserliche  Akademie  der 

Wissenchaften  (Wien).      [Each  volume  contains 

2  or  3  parts  (Abt/ieilungen) ;  each  part  is  bound 

and  paged  as  a  separate  volume  ;  the  arrange- 
ment is  perplexing.] 
Sitzungsberichte  der  Akademie  der  Wissenschaften 

zu  Berlin.     [1854,  and  onwards.] 
Jahresberichte  ilber  die  Fortschritte  der  Chemie,  &c. 

[Since   1873,   Staedel  has  edited  a  very  useful 

Jahresber.  ilber  die  Fortschritte  aitf  dem  Gebiete 

der  Reinen  Chemie.'] 
Comptes    rendtis    hebdomadaires    des    Seances    de 

fAcademie  des  Sciences.     [1835,  onwards.] 
Memoires  de  F Academic    Royale  des  Sciences  de 

r Institut  de  France.     [1816,  onwards.] 
Annales  de  Chimie  et  de  Physique.    [Series  1  to  6.] 
Bulletin  de  la  Societe  Chimique  de  Paris.     [1864, 

onwards.] 
Memoires  de  Physique  et  de  Chimie  de  la  Societe 

cfArcueil.     [3  vols.  1807-1817.] 
Memoires    couronnes  par    F Academic  royale  des 

Sciences  et  Belles- Lettres  de  Bruxelles.     [1827, 

onwards.] 
Annales  des  Mines.     [Series  1  to  6.] 


CORRECTIONS   AND   ADDITIONS. 


PAGE 

22.     Bottom  line  ;  for  '  186 '  read  '  i8'6 '. 

38.  Second  line  from  top  ;  for  '  phosphorous '  read  '  phosphorus '. 

39.  Between  fourth  and  fifth  line  from  bottom  ;  insert 

<4a  Beryllium  chloride  |  2*93  |  8173  |  79-84  |  9*1  beryllium  +  70*84  chlorine'. 

41.     At  end  of  note  4  ;  insert  t4*  See  Nilson  and  Pettersson,  Ber.  17.  987  '. 
41.     At  end  of  notes  ;  insert  '  V.  Meyer  (Ber.  17.  1335)  has  obtained  numbers 
which  seem  to  indicate  that  gaseous  ferrous  chloride  at  low  temperatures 
consists  of  molecules  of  Fe2Cl4,  and  at  high  temperatures  of  molecules  of 
FeCl2'. 
63.     Line  20  from  top ;    before  '  Kopp's  hypothesis '  insert  '  With  regard  to  ' 

and  dele  from  'will  be  again'  to  'meanwhile'  (both  inclusive). 
76.     At  end  of  note  i ;  add  'also  ibid.  17.  1335  '. 

78.     In  second  column  opposite  BERYLLIUM  ;  for  '  none '  read  '  BeCl2 '. 
90.     Note;  after  'Book  II.  chap,  n.'  insert  'par.  189'. 
148.     Note  j  for  '  loc.  citS  read  '  Organic  Chemistry '. 
190.     Note ;  for  '  Book  n.  chap.  II.'  read  '  Book  n.  chap,  i.' 
208.     Note  i  ;  add  '  See  also  Report  of  the  B.  A.  committee  on  Spectrum  Analysis. 

Brit.  Ass.  Reports  for  1880.  258  ;  especially  pp.  284—298'. 
214.     Note  i  ;  to  references  to  work  on  cryohydrates,  add  '18.  22  '. 
229.     Note  i  ;  add  'But  see  Carnelley,  Ber.  17.  1357'. 
269.     Note  2  ;  dele  [2]. 

294.     Third  line  from  top  ;  for  '  combination '  read  '  oxidation'. 
297.     Seventh  line  from  top  ;  for  '  term  '  read  '  terms '. 

300.     Ninth  line  from  bottom  ;  for  '  (stone  or  system) '  read '  stone  (or  system) '. 
324.     Seventh  line  from  bottom ;  for  '  (RaR^) '  read  *  (R2R2)  C '. 
372.     Seventh  line  from  bottom  ;  for  '  relation  '  read  '  relations  '. 
451.     Note;  add  '  See  also  ibid.  Phil.  Mag.  (5).  18.  233'. 


"  L'action  chimique  est  reciproque  :  son  effet  est  le  resultat  d'une  tendance 
mutuelle  a  la  combinaison  ;  on  ne  pent  pas,  a  la  rigeur,  dire  plutot  qu'un  liquide 
agit  sur  un  solide,  qu'on  ne  peut  dire  que  le  solide  agit  sur  le  liquide  :  la 
commodite  de  1'expression  fait  transporter  sans  inconvenient  toute  1'action  dans 
1'une  des  deux  substances,  quand  on  veut  examiner  1'effet  de  cette  action  plutot 
que  1'action  elle-meme."  BERTHOLLET. 


INTRODUCTORY. 


CHEMISTRY  is  preeminently  the  science  which  concerns 
itself  with  the  changes  presented  in  material  phenomena ;  it 
is  the  science  which  attempts  to.  classify  the  mutations  that 
matter  undergoes. 

In  the  chemical  examination  of  any  kind  of  matter  two 
questions  have  always  pressed  for  answers : — What  can  this 
substance  do  ?  Of  what  is  this  substance  composed  ?  While 
attempting  to  answer  these  questions  separately,  and  while 
thus  more  or  less  adopting  two  schemes  of  classification, 
chemists  have  for  the  most  part  recognised  that  no  complete 
answer  could  be  given  to  either  question  considered  wholly 
apart  from  the  other ;  hence  the  two  methods  of  chemical 
investigation,  and  the  two  lines  of  chemical  advance  have 
generally  been  closely  interwoven. 

In  older  times  a  substance  was  said  to  be  capable  of 
doing  this  or  that  because  it  contained  certain  elements  or 
essences ;  substances  were  classed  together  because  of  simi- 
larity of  actions,  but  the  points  of  resemblance  on  which 
classification  was  based  were  uncertain  and  undefined  : — the 
conception  of  element  was  paramount.  The  substances  in 
a  class  shewed  many  or  a  few  points  of  resemblance  because 
each  member  of  the  class  contained  the  same  element,  and 
hence  was  a  more  or  less  perfect  means  for  exhibiting  the 
properties  of  that  element.  The  ideas  of  composition  and 
properties,  as  we  now  use  these  expressions,  were  both  im- 
plied in  the  older  conception  of  element. 

M.  c.  I 


2  INTRODUCTORY. 

If  it  be  granted  that  the  various  forms  of  matter  are 
vehicles  for  displaying  the  properties  of  a  few  elements,  it 
follows  that  the  addition  or  withdrawal  of  this  or  that  ele- 
ment will  probably  suffice  to  change  one  into  another  form 
of  matter.  Hence  arose  the  art  of  alchemy  and  the  pursuit 
of  the  philosopher's  stone.  This  pursuit  resulted  in  the  ac- 
cumulation of  many  facts  most  of  which  could  for  some  time 
be  explained  by  aid  of  the  one  underlying  general  concep- 
tion of  element.  But  as  facts  accumulated  the  foundation 
was  found  to  be  too  narrow  to  bear  the  structure  raised  upon 
it ;  a  need  was  felt  for  minor  explanations  and  for  partial 
hypotheses.  Observers  began  to  contrast  sour,  acid  sub- 
stances with  mild,  tasteless,  non-corrosive  substances;  hence 
arose  the  division  of  a  large  class  of  bodies  into  two  minor 
classes,  acids  and  alkalis.  This  classification  when  carried 
to  completion  produced  the  school  of  ztf/r0-chemists,  in 
whose  hands  chemical  science  became  a  branch  of  the  art 
of  medicine.  But  once  again  facts  were  observed  which 
could  not  be  explained  by  the  theories  of  the  medical 
chemists :  the  experimental  method  was  recognised  as  alone 
leading  to  definite  and  trustworthy  results  in  the  examination 
of  natural  phenomena ;  but  the  experimental  method,  it  was 
found,  to  be  of  value  must  be  accurate,  and  to  be  accurate 
must  be  quantitative.  Advance  became  rapid.  The  con- 
ception of  element  remained  but  in  modified  form,  the  dis- 
tinction between  alkali  and  acid  remained,  but  proved  to 
mean  at  once  less  and  more  than  its  originators  supposed. 
Bodies  were  compared  as  to  their  actions  and  as  to  their 
compositions ;  the  comparison  led  on  one  hand  to  the  recog- 
nition of  force  exerted  by  one  body  on  another,  called  affinity, 
and  on  the  other  hand  to  the  recognition  of  ultimate  forms  of 
matter,  called  elements,  of  which  all  bodies  are  composed. 

From  this  point  the  two  broad  paths  of  advance  become 
more  easily  distinguished ;  advance  is  made  by  seeking 
answers  to  questions  such  as  these : — What  is  the  nature 
of  the  elements?  What  is  the  composition  of  compounds? 
Can  the  facts  regarding  elementary  combinations  be  general- 
ised ?  Advance  is  also  made  by  pursuing  inquiries  indicated 


INTRODUCTORY.  3 

by  such  questions  as  these  : — What  connection,  if  any,  exists 
between  the  properties  of  elements  and  of  compounds  of  these 
elements  ?  What  actions  are  these  compounds  capable  of 
performing  ?  And  advance  is  also  made  by  combining  both 
methods  of  inquiry  in  seeking  answers  to  such  a  question  as 
this : — Why  are  the  properties  of  these  compounds  such  as 
they  are  observed  to  be  ? 

At  one  time  those  chemists  for  whom  the  composition  of 
compounds  was  all-important  have  been  supreme ;  at  another 
time  the  place  of  authority  has  been  occupied  by  those  who 
regarded  function,  or  power  of  doing,  as  the  essential  subject 
of  study.  The  greatest  outcome  of  the  work  of  the  former 
school  is  the  atomic  hypothesis,  now  merged  in  the  wider 
molecular  theory  of  matter  ;  the  most  important  result  of  the 
studies  of  the  latter  school  is  the  conception  of  chemical 
affinity;  both  have  taken  part  in  the  development  of  the 
modern  views  regarding  molecular  structure  and  rational 
formulae. 

While  assigning  the  credit  of  special  advances  to  one  of 
the  two  great  schools  of  chemistry,  we  cannot  but  recog- 
nise that  these  advances  have  been  made  by  the  help  of 
suggestions  borrowed  from  the  other ;  recent  developments 
of  the  atomic  theory  cannot  be  separated  from  the  rise  of  the 
unitary  system,  the  latest  hypotheses  regarding  the  structure 
of  molecules  are  connected  with  the  subject  of  chemical 
affinity. 

Eighty  years  ago  Berthollet  attempted  to  arrange  the 
facts  of  chemical  action  under  a  general  conception  which 
should  serve  to  connect  chemical  with  physical  changes  ;  but 
the  attempt  was  only  partially  successful  because  of  the  scanty 
supply  of  purely  chemical  data.  General  views  of  chemical 
action  were  soon  abandoned  for  a  study  of  the  properties  of 
the  products  of  this  action,  but  of  late  years  many  chemists 
have  resumed  the  investigation  of  the  general  conditions  of 
chemical  action,  and  have  obtained  results  which  give  good 
grounds  for  hoping  that  this  study  will  throw  light  on  the 
masses  of  facts  already  accumulated  concerning  compounds, 
and  groups  of  compounds,  and  taken  along  with  that  method 

I — 2 


4  INTRODUCTORY. 

of  investigation  which  is  based  on  a  study  of  the  composition 
of  compounds,  will  lead  to  the  establishment  of  chemistry  as 
a  branch  of  the  science  of  dynamics. 

The  study  of  the  motions  of  material  bodies  considered  as 
accompanying  mutual  actions  between  these  bodies  belongs 
to  the  general  science  of  dynamics.  Phenomena  presented 
by  mutually  acting  bodies  wherein  the  properties  of  these 
bodies  are  not  profoundly  modified,  belong  to  the  domain  of 
physical  science.  Chemistry  deals  with  those  reactions 
between  bodies  wherein  profound  modifications  in  the  pro- 
perties of  the  bodies  occur.  Or,  we  may  say  that  whereas 
physical  science  is  concerned  with  the  properties  of  this  or 
that  kind  of  matter  considered  for  the  most  part  apart  from 
the  action  on  it  of  other  kinds  of  matter,  chemistry  is  con- 
cerned with  the  mutual  actions  which  occur  between  matter 
of  different  kinds  whereby  persistent  changes  in  the  properties 
of  the  reacting  kinds  of  matter  occur. 

Chemistry  furnishes  problems  for  the  solution  of  which 
physical  and  dynamical  methods  are  applicable.  Chemical 
science  is  ever  tending  toward  abstract  truths,  i.  e.  truths 
involved  in  many  phenomena  although  actually  seen  in  none  : 
but  before  she  gains  abstract  truths  chemistry  amasses  many 
general  truths,  i.e.  'truths  which  sum  up  many  facts1.' 

The  chemist  is  set  to  solve  the  problem, — Why  are  the 
properties  of  bodies  profoundly  modified  under  certain  con- 
ditions ?  In  attempting  to  find  a  solution,  he  must  divide  the 
phenomena  which  he  observes  into  their  factors,  and  study 
each  of  these  as  far  as  possible  independently  of  the  others. 

The  chemist  need  not  regard  the  methods  pursued  by 
those  sciences  which  are  more  concrete  than  his  own, 
although  he  may  furnish  them  with  subject-matter  for  in- 
vestigation ;  inasmuch  however  as  the  science  of  matter  and 
motion  is  a  more  abstract  science  than  that  of  chemistry,  he 
must  seek  help  for  his  work  in  the  methods  of  that  science, 

1  The  abstract  and  the  general  truths  of  chemistry  are  scarcely  yet  so 
differentiated  as  to  allow  of  each  class  being  considered  separately.  I  do  not 
purpose  attempting  more  than  a  very  rough  separation  in  this  book. 


INTRODUCTORY.  5 

always  remembering  that  this  help  is  given  to  solve  chemical 
problems,  and  that  with  purely  physical  problems,  he,  as  a 
chemist,  is  not  concerned1. 

Pursuing  then  an  almost  purely  analytical  method  the 
chemist  finds  that  his  subject  branches  off  into  two  main 
divisions.  The  properties  of  bodies  are  modified  : — he  studies 
the  relations  between  the  new  substances  and  those  by  the 
mutual  action  of  which  the  new  bodies  were  produced  ;  but 
changes  in  the  properties  of  bodies  involve  a  consideration  of 
the  relative  positions  of  the  changing  body  and  of  other 
bodies, — involve  the  action  of  force : — he  endeavours  to 
elucidate  the  laws  of  action  of  this  force. 

The  hypothesis  that  bodies  consist  of  small  parts — called 
molecules — in  motion,  is  one  of  the  lines  along  which  dy- 
namical science  pursues  its  advance  into  the  sphere  of 
chemistry.  The  study  of  chemical  phenomena  is  also 
brought  within  the  pale  of  dynamical  methods  by  the  appli- 
cation to  these  phenomena  of  the  general  principles  of  the 
conservation  and  degradation  of  energy2.  The  latter  (therm  o- 
dynamic)  method  is  more  applicable  to  the  study  of  the  laws 
of  chemical  forces  than  of  the  properties  of  the  substances 
depending  on  the  actions  of  these  forces,  which  properties  have 
been  chiefly  elucidated  by  the  help  of  the  molecular  theory. 

We  may  indeed  study  relations  between  forces  accom- 
panying changes  in  the  distribution  of  certain  material  magni- 
tudes, which  we  may  call  molecules,  without  reference  to 
what  is  generally  known  as  the  molecular  theory  of  matter. 

But  it  seems  certain  that  no  chemical  phenomenon — and  it 
is  well  for  the  student  to  bear  in  mind  that  the  chemical  part 
is  always  but  one  aspect  of  any  natural  occurrence — can  be 
fully  explained  unless  both  methods  of  investigation  are 
applied  ;  unless  the  relations  between  the  reacting  bodies  and 
the  products  of  the  reaction,  and  the  relations  between  the 
forces  exhibited  in  the  phenomenon  in  question,  are  con- 
sidered. 

1  Chemistry,  being  more  concrete,  is  less  exact  than  Physics ;  mathematical 
methods  can  scarcely  as  yet  be  applied  to  chemical  data. 

2  See  Clerk  Maxwell:  Science  Conferences  at  South  Kensington,  1876. 


6  INTRODUCTORY. 

In  the  following  pages  an  attempt  is  made  to  gather 
together  the  more  important  data  on  which  the  leading 
generalisations  of  chemistry  are  based,  and  in  the  light  of  this 
material  to  discuss  these  generalisations. 

By  the  use  of  the  terms  Chemical  Statics  and  Chemical 
Kinetics  I  endeavour  to  indicate,  roughly,  that  the  phenomena 
included  under  the  first  of  these  headings  are  on  the  whole 
those  exhibited  by  chemical  bodies  or  systems  of  bodies  in 
equilibrium,  while  the  phenomena  classed  together  as  chemi- 
cal kinetics  relate  more  to  bodies  or  systems  of  bodies  when 
chemically  active. 

It  may  seem  pedantic  to  make  use  of  terms  having  definite 
and  precise  significations  when  from  the  very  nature  of  the 
facts  they  can  be  employed  only  in  the  broadest  and  roughest 
way.  I  only  wish  to  indicate  that  the  subject-matter  of 
chemical  science  is  considered  in  this  book  as  divisible  into 
two  large  parts,  of  which  one  comprises  the  facts  and 
principles  concerned,  on  the  whole,  with  chemical  com- 
position, and  the  other  those  which,  broadly  speaking,  relate 
to  chemical  action. 

It  will  of  course  be  found  that  chemical  occurrences 
present,  I  think  one  may  say  always  present,  both  statical 
and  kinetical  problems ;  the  two  sides  of  any  chemical 
problem  can  scarcely  be  regarded  apart,  in  the  present  state 
of  knowledge  at  any  rate,  without  danger ;  it  may  there- 
fore be  that  phenomena  ranked  by  one  chemist  as  statical 
would  by  another  be  classed  as  kinetical. 

I  begin  by  considering  the  facts  and  principles  roughly 
classed  as  statical,  because  although  the  study  of  kinetics 
seems  naturally  to  precede  that  of  statics,  yet  in  chemistry 
our  knowledge  of  composition  is  much  in  advance  of  our 
knowledge  of  action  :  I  then  consider  the  data  and  generalisa- 
tions of  so-called  chemical  kinetics ;  and  lastly  I  endeavour 
to  review  some  of  those  phenomena,  explanations  of  which, 
generally  only  very  partial  explanations,  can  be  gained,  or 
hoped  for,  only  by  the  help  of  both  methods. 


BOOK    I. 
CHEMICAL   STATICS. 

CHAPTER   I. 

ATOMS  AND   MOLECULES. 

I.  THE  foundations  of  the  atomic  theory  were  laid  in  the 
later  years  of  last  century  by  the  German  chemist  RlCHTER1. 
The  work  of  BERGMANN2,  although  of  earlier  date  than  that 
of  Richter,  cannot  be  regarded  of  equal  importance  as  concerns 
the  history  of  the  atomic  theory. 

Richter  studied  the  neutralisation  of  acids  by  bases,  and  of 
bases  by  acids,  and  shewed  that  a  definite  amount  of  acid  (or 
base)  always  combines  with  a  definite  amount  of  base  (or 
acid)  when  neutralisation  is  accomplished.  By  determining 
the  weights  of  various  bases  neutralised  by  one  and  the  same 
weight  of  each  acid,  and  the  weights  of  various  acids  neutral- 
ised by  one  and  the  same  weight  of  each  base,  Richter 
was  able  to  arrange  many  acids  and  bases  in  order  of 
neutralisation.  FISCHER3,  in  1803,  published  the  first  table  of 
chemical  equivalents.  Richter  had  given  a  series  of  numbers 
for  each  base  expressing  the  quantities  thereof  which  would 
neutralise  1000  parts  of  sulphuric,  hydrochloric,  nitric  &c.  &c. 
acids ;  Fischer  saw  that  it  was  sufficient  to  attach  a  single 
number  to  each  base  and  a  single  number  to  each  acid,  1000 
parts  of  sulphuric  acid  being  adopted  as  the  unit  of  neutralisa- 
tion. Fischer's  numbers  expressed  quantities  of  bases,  or 

1  Ueber  die  neueren  Gegenstiinde  der  Chemie,  1791 — 1802  :  and  Anfangsgrunde 
der  Stochiometrie  oder  Messkunst  chemischer  Element e,  1822. 

2  Chemise  he  Werke,  2.  25  et  seq. 

3  In  a  note  to  Berthollet's  Essaide  Statique  Chimique. 


8  CHEMICAL   STATICS.  [§  2 

acids,  which  were  of  equal  value  so  far  as  power  to  neutralise 
a  constant  weight  of  a  certain  acid  or  base  was  concerned1. 

Foreshadowings  of  the  atomic  theory  are  to  be  found  in  a 
work  by  W.  HiGGlNS  entitled  A  comparative  view  of  the 
Phlogistic  and  Antiphlogistic  Theories,  with  Inductions  (1791) 
[see  Henry's  Life  of  Dalton  p.  75  et  seq]  but  to  DALTON  is 
undoubtedly  due  the  signal  honour  of  introducing  a  clear  and 
self-consistent  theory  regarding  the  composition  and  structure 
of  chemical  substances,  a  theory  which  in  its  essential  points 
has  stood  the  test  of  rigorous  experimental  verification,  and 
has  adapted  itself  to  the  wants  of  each  successive  school  of 
chemical  thought. 

2.  Dalton2,  and  others,  found  that  elements  were  united  in 
many  compounds  in  fixed  proportions  by  weight,  and  more- 
over that  in  certain  compounds  of  one  element  with  others 
the  amount  by  weight  of  this  element  could  be  expressed  by 
whole  multiples  of  one  fundamental  number3.  To  account 
for  these  facts  Dalton  recalled  the  atomic  theory  of  the.  Greek 
philosophers ;  but  he  introduced  accuracy  where  there  had 
been  vagueness.  From  an  interesting  intellectual  plaything 
Dalton's  genius  produced  an  exact  scientific  theory  capable  of 
experimental  application. 

Every  chemical  substance,  simple  or  compound,  is  made 
up  of  atoms,  or  small  undivided  parts4; — the  old  hypothesis 
had  gone  nearly  as  far  as  this :  Dalton  added,  the  atom  of 
every  chemical  substance  has  a  definite  weight,  and  although 
this  weight  cannot  be  determined,  we  nevertheless  can 
determine  the  relative  weights  of  the  atoms  of  all  bodies.  It 

1  For  more  details  regarding  the  work  of  Richter  and  Fischer,  see  Wurtz,  The 
Atomic  Theory,  pp.  12 — 22. 

2  It  is  important  to  note  that  the  atomic  theory  was  conceived  by  Dalton  in 
1802  from  considering  the  results  of  physical  experiments  :  he  distinctly  states  in 
a  paper  on  the  absorption  of  gases  in  liquids  read  to  the  Manchester  Philosophical 
Society   in    that   year   that   he   had    lately  been   prosecuting   'with  remarkable 
'success,'  'an  inquiry  into  the  relative  weights  of  the  ultimate  particles  of  bodies.' 

3  For  examples  of  this  law  of  multiple  proportions  see  Roscoe  and  Schorlem- 
mer's  Treatise  on  Chemistry,  1.  pp.  60 — 65. 

4  Dalton's  application  of  the  term  atom  to  the  small   chemically  indivisible 
parts  of  compounds,  seems  to  shew  that  he  did  not  regard  his  atoms  as  absolutely 
indivisible  ;  see  Life  by  Henry,  p.  88. 


§  2]  ATOMS  AND   MOLECULES.  9 

is  only  necessary  to  choose  some  substance  as  a  standard,  then 
the  weight  of  the  smallest  quantity  of  any  other  substance 
which  combines  with  the  unit  weight  of  the  standard  substance 
represents  the  weight  of  the  atom  of  the  combining  substance 
in  terms  of  the  unit  chosen. 

As  this  point  is  of  supreme  importance  it  may  be  well 
that  we  should  have  Dalton's  own  words  before  us.  In  the 
New  System  of  Chemical  Philosophy  (1808)  after  discussing 
the  constitution  of  mixed  gases,  Dalton  proceeds:  'When 
'  any  body  exists  in  the  elastic  state  its  ultimate  particles  are 
'  separated  from  each  other  to  a  much  greater  distance  than 
'  in  any  other  state ;  each  particle  occupies  the  centre  of  a 
'comparatively  large  sphere,  and  supports  its  dignity  by 
'  keeping  all  the  rest,  which  by  their  gravity  or  otherwise  are 
'  disposed  to  encroach  upon  it,  at  a  respectful  distance.  When 
'  we  attempt  to  conceive  the  number  of  particles  in  an  atmo- 
'  sphere,  it  is  somewhat  like  attempting  to  conceive  the  number 
'  of  stars  in  the  universe  ;  we  are  confounded  by  the  thought. 
'  But  if  we  limit  the  subject,  by  taking  a  given  volume  of  any 
'gas,  we  seem  persuaded  that,  let  the  divisions  be  ever  so 
'  minute,  the  number  of  particles  must  be  finite;  just  as  in  a 
'  given  space  of  the  universe  the  number  of  stars  and  planets 
'  cannot  be  infinite. 

'  Chemical  analysis  and  synthesis  go  no  further  than  to 
'the  separation  of  particles  one  from  another,  and  to  their 
*  reunion.  No  new  creation  or  destruction  of  matter  is  within 
'  the  reach  of  chemical  agency.  We  might  as  well  attempt  to 
'  introduce  a  new  planet  into  the  solar  system,  or  to  annihi- 
late one  already  in  existence,  as  to  create  or  destroy  a 
'particle  of  hydrogen.  All  the  changes  we  can  produce 
'  consist  in  separating  particles  that  are  in  a  state  of  cohesion 
'  or  combination,  and  joining  those  that  were  previously  at  a 
'  distance. 

'  In  all  chemical  investigations  it  has  justly  been  consider- 
'  ed  an  important  object  to  ascertain  the  relative  weights  of 
'  the  simples  which  constitute  a  compound.  But  unfortunately 
'thxi  inquiry  has  terminated  here  ;  whereas  from  the  relative 
'weights  in  the  mass,  the  relative  weights  of  the  ultimate 


10  CHEMICAL   STATICS.  [§  2 

'  particles  or  atoms  of  the  bodies  might  have  been  inferred, 
'  from   which   their   number   and    weight    in    various    other 

*  compounds   would  appear,  in  order  to  assist  and  to  guide 
'  future  investigations,  and  to  correct  their  results.     Now  it  is 
'  one  great  object  of  this  work,  to  shew  the  importance  and 
1  advantage  of  ascertaining  the  relative  weights  of  the  ultimate 
'  particles  both  of  simple  and  compound  bodies,  the  number  of 

*  simple  elementary  particles  which  constitute  one  compound 

*  particle,  and  the  number  of  less  compound  particles  which 
'  enter  into  the  formation  of  one  more  compound  particle. 

'  If  there  are  two  bodies,  A  and  B,  which  are  disposed  to 
'  combine,  the  following  is  the  order  in  which  combination 
'  may  take  place,  beginning  with  the  most  simple  :  namely — 

'  I  atom  of  A  +  I  atom  of  B  —  I  atom  of  C,  binary, 
'I     „       „  A  +  2  atoms  „  B  =  I      „      „  D,  ternary, 
'  2  atoms  „  A  +  I  atom  „  B  =  I      „      „  E>  ternary, 
'  I  atom   „  A  -f  3  atoms  „  B  =  I      „      „  F,  quaternary, 
'  3  atoms  „  A  -f  I  atom    ,,5  =  1       „      „  G,  quaternary.' 
&c.,  &c. 

Dalton  then  states  the  following  rules  respecting  chemical 
synthesis,  which  he  employed  in  determining  the  relative 
weights  of  the  smallest  chemically  indivisible  parts  of  com- 
pound bodies  *. 

1  1st.  When  only  one  combination  of  two  bodies  can  be 
'  obtained,  it  must  be  presumed  to  be  a  binary  one,  unless 
'  some  cause  appears  to  the  contrary. 

'  2nd.  When  two  combinations  are  observed  they  must  be 
'  presumed  to  be  a  binary  and  a  ternary. 

1  3rd.  When  three  combinations  are  obtained,  we  may 
'  expect  one  to  be  a  binary ',  and  the  other  two  ternary. 

'4th.  When  four  combinations  are  observed,  we  should 
'  expect  one  binary,  two  ternary ',  and  one  quaternary!  &c.  &c. 

'From  the  application  of  these  rules,'  Dalton  says,  'to  the 
'  chemical  facts  already  well  ascertained,  we  deduce  the  follow- 

1  By  the  '  smallest  chemically  indivisible  part '  of  a  substance  is  meant  an 
amount  such  that,  if  divided,  substances  (or  a  substance)  are  produced  different  in 
properties  from  the  original  substance. 


§  3]  ATOMS  AND   MOLECULES.  1 1 

'  ing  conclusions :  ist.  That  water  is  a  binary  compound  of 
1  hydrogen  and  oxygen,  and  the  relative  weights  of  the  two 
'  elementary  atoms  are  as  I  :  7  nearly.  2nd.  That  ammonia 
'  is  a  binary  compound  of  hydrogen  and  azote,  and  the  relative 
'weights  of  the  two  atoms  are  as  I  :  5  nearly — In  all  these 
1  cases  the  weights  are  expressed  in  atoms  of  hydrogen  each 
'  of  which  is  denoted  by  unity.' 

Two  oxides  of  carbon  were  known  to  Dalton,  containing 
according  to  him,  5-4  parts  by  weight  of  carbon  combined 
respectively  with  7  and  with  14  parts  by  weight  of  oxygen : 
the  first  of  these  bodies,  in  accordance  with  Dalton's 
second  rule,  was  considered  to  be  a  binary,  and  the  second 
a  ternary  compound  ;  the  formulae  given  were  CO  and  CO2 
respectively.  [C  =  5-4,  O  =  7.] 

But  Dalton's  CO2  might  have  been  regarded  as  a  com- 
pound of  27  parts  by  weight  of  carbon  with  7  parts  by 
weight  of  oxygen,  in  which  case  its  formula  would  have 
been  written  CO  [C=2'7];  Dalton's  CO  would  then  have 
become  C2O  [C2=  5*4].  The  atomic  weight  of  carbon  would 
be  determined  as  27  or  5*4  according  as  carbon  monoxide 
or  carbon  dioxide  was  decided  to  be  a  binary  compound. 

At  a  later  time  it  was  said  by  some  chemists  that  a  binary 
compound  is  always  more  stable  than  a  ternary  ;  if  this  rule 
were  applied  to  the  case  of  the  oxides  of  carbon,  Dalton's 
number  for  the  atomic  weight  of  carbon  would  be  confirmed1. 

3.  These  examples  illustrate  the  great  shortcoming  of 
the  Daltonian  theory  :  the  atomic  weights  of  Dalton  are 
either  multiples  or  submultiples  of  a  certain  number,  but  we 
cannot  tell  what  multiple  or  what  submultiple.  Let  the 
relative  weights  of  two  elements,  hydrogen  being  taken  as 
unity,  which  form  a  compound  B,  be  Q  and  Qv  and  let  the 
atomic  weights  of  these  elements  be  A  and  Al  respectively, 
then  Q  :  Q1  ::  nA  :  n^Av  where  n  and  n^  are  whole  numbers. 
But  inasmuch  as  the  values  of  ;/,  ;/lf  A,  and  Al  are  unknown 
it  is  evident  that  analysis  alone,  aided  by  the  Daltonian 
theory,  cannot  determine  the  atomic  weights  of  the  elements 
which  compose  the  substance  B. 

1  See  especially  Daubeny's  Atomic  Theory  (?nd  edition  1850),  pp.  119—120. 


, , 


12  CHEMICAL   STATICS.  [§§4,  5 

This  shortcoming  in  the  theory  could  not  be  supplied 
without  further  data  :  Dalton  distinctly  states  that  in  order  to 
determine  the  number  of  elementary  atoms  in  the  atom  of  a 
compound  a  knowledge  of  the  composition  of  many  com- 
pounds of  the  given  elements  is  required. 

4.  A  few  months  after  the   announcement   of  Dalton's 
law  of  multiple  proportions  and  atomic  theory,  GAY  LUSSAC 
and  HuMBOLDT1  began  their  volumetric  investigations  which 
culminated   three   years   later   in  the  beautiful  discovery  of 
the  former  naturalist2,  that  gaseous  substances  unite  in  fixed 
volumetric  proportions  which  may  be  simply  expressed. 

There  is  a  constant  simple  relation,  said  Gay  Lussac, 
between  the  volume  of  a  gaseous  compound  and  the  volumes 
of  its  constituent  elements.  Let  one  volume  be  defined  as 
the  volume  occupied  by  one  part  by  weight  of  hydrogen,  then 
the  combining  volume  of  any  gaseous  element  is  always 
expressed  by  a  whole  number,  e.g.  one  volume  of  nitrogen 
combines  with  one  volume  of  oxygen  to  form  two  volumes  of 
nitric  oxide;  two  volumes  of  hydrogen  and  one  volume  of 
oxygen  combine  to  form  two  volumes  of  water-gas ;  one 
volume  of  nitrogen  and  three  volumes  of  hydrogen  form  two 
volumes  of  ammonia,  &c.  &c.  Condensation  sometimes  occurs, 
sometimes  the  volume  of  the  compound  is  equal  to  the  sum 
of  the  volumes  of  the  combining  elements. 

This  discovery  appeared  to  add  fresh  arguments  to  the 
theory  of  Dalton.  The  ratios  of  the  weights  of  these  com- 
bining volumes  of  the  elements,  hydrogen  being  taken  as 
unity,  represent,  it  was  said,  the  relative  weights  of  the  atoms 
of  these  elements ;  and  the  conclusion  was  drawn,  '  equal 
volumes  of  gaseous  substances,  measured  at  the  same  tem- 
perature and  pressure,  contain  equal  numbers  of  atoms.' 

5.  Dalton    however    refused    to    accept    Gay    Lussac's 
generalisation,  and   regarded   his  experimental    methods    as 
untrustworthy.     We  cannot,  I  think,  fail  to  be  struck   with 
the  justness  of  Dalton's  objection  to   the   statement   *  equal 
volumes  contain  equal  numbers  of  atoms  :'  he  argued  some- 
what as  follows : — One  volume  of  nitrogen  and  one  volume 

1  Journal  de  Physique,  60.  129.  2  Mem.  de  la  Soc.  d'Arcueil\  2.  207. 


§6]  ATOMS   AND   MOLECULES.  13 

of  oxygen  form  two  volumes  of  nitric  oxide ;  but  one  atom 
of  nitrogen  and  one  atom  of  oxygen  form  one  atom  of  nitric 
oxide ;  therefore,  had  the  above  statement  been  correct,  the 
volume  of  nitric  oxide  would  have  been  equal  to,  not  twice 
as  great  as  the  volume  of  oxygen  or  of  nitrogen.  So  again, 
one  atom  of  hydrogen  and  one  atom  of  oxygen  form  one 
atom  of  water,  according  to  Dalton's  rules :  but  Gay  Lussac 
shewed  that  two  volumes  of  hydrogen  combine  with  one  volume 
of  oxygen  to  produce  two  volumes  of  water-gas ;  hence  the 
atom  of  hydrogen  occupies  twice  the  volume  occupied  by  the 
atom  of  oxygen,  and  therefore  the  statement  of  Gay  Lussac 
is  incorrect.  If  Dalton's  definition  of  atom  and  his  rules 
regarding  atomic  synthesis  are  adopted  Gay  Lussac's  state- 
ment that  'equal  volumes  contain  equal  numbers  of  atoms' 
must  be  abandoned. 

6.  The  difficulty  was  removed  by  AVOGADRO1,  who  (in 
1811)  introduced  the  idea  of  two  kinds  of  atoms  : — 'molecules 
'  integrantes]  or  as  we  should  now  say  molecules;  and  '  molecules 
'  elementairesl  or  as  we  should  now  say  atoms. 

The  molecules  of  elements  are  decomposed  in  chemical 
processes,  said  Avogadro,  and  the  atoms  unite  to  form  new 
compounds.  'Equal  volumes  of  gases  contain  equal  numbers 
'of  molecules!  The  reaction  between  nitrogen  and  oxygen 
inexplicable  by  Gay  Lussac's  law  now  becomes  clear ;  each 
molecule  of  nitrogen  and  each  molecule  of  oxygen  divides 
into  two  parts,  and  these  parts  unite  to  form  the  new  mole- 
cules of  nitric  oxide,  hence  there  are  twice  as  many  mole- 
cules of  nitric  oxide  produced  as  there  were  molecules  of 
nitrogen  or  oxygen  originally  present. 

By  thus  recognising  a  higher  order  of  atoms,  as  it  were, 
Avogadro  reconciled  Dalton's  theory  with  Gay  Lussac's  results. 

Ampere2  in  1814  drew  prominent  attention  to  the  hypo- 
thesis of  Avogadro,  and  attempted  by  its  help  to  explain  the 
structure  of  crystals.  But  the  hypothesis  had  come  before 
the  times  were  fully  ripe. 

1  Journal  de  Physique,  73.  58  :  also  Essai  d'une  maniere  de  determiner  Its 
masses  relatives  des  molecules  clementaires  des  corps ;  &c. 

2  Ann.  Chim.  Phys.  90.  43. 


14  CHEMICAL   STATICS.  [§  / 

7.  WOLLASTON l  accepted  Dalton's  theory  but  proposed 
to  use  the  word  equivalent*  in  place  of  atom.  In  his  paper 
published  in  1814  (loc.  tit.)  Wollaston  drew  up  a  table  of 
equivalents  which  he  thought  would  be  serviceable  to  the 
practical  chemist  in  determining  the  amount  of  an  acid  which 
would  combine  with  a  given  weight  of  base,  or  the  weight  of 
precipitate  obtainable  in  a  given  reactio'n,  &c.  He  arranged 
his  numbers  on  a  scale  with  a  slider  attached,  and  adopted  a 
mechanical  contrivance  for  aiding  the  analyst  in  using  the  table. 
Although  Wollaston  employed  the  word  equivalent  in  place 
of  atom,  his  scale  and  table  must  be  regarded  as  helping  to 
extend  the  use  of  the  atomic  theory3.  For  the  practical  purpose 
which  he  had  in  view  Wollaston  did  not  deem  it  necessary  to 
adopt  any  theory ;  at  the  same  time  he  regarded  the  atomic 
weights  of  Dalton,  especially  the  atomic  weights  of  compounds, 
as  too  hypothetical,  and  he  thought  that  equivalents  were  to 
be  preferred  for  most  purposes. 

Wollaston  referred  his  equivalent  numbers  to  oxygen  as 
10  :  the  amount  by  weight  of  any  element  which  combined 
with  10  parts  by  weight  of  oxygen  was  regarded  by  him  as 
the  equivalent  of  that  element.  But  the  system  of  equiva- 
lents was  liable  to  the  same  objection  as  had  been  urged 
against  the  system  of  atomic  weights  ; — it  was  too  vague. 

(1)  7*5  parts  by  weight  of  carbon  unite  with  20  parts  by 
weight  of  oxygen,  said  Wollaston,  therefore  the  formula  of  the 
compound  produced  is  CO2. 

(2)  Again  7*5  parts  by  weight  of  carbon  unite  with  10 
parts  by  weight  of  oxygen,  therefore  the  formula  of  the  com- 
pound produced  is  CO. 

But  he  might  also  have  said 

(0  375  parts  by  weight  of  carbon  unite  with  10  parts 
by  weight  of  oxygen,  and  the  formula  of  the  product  is 
CO;  and 

(2)  7*5  of  carbon  unite  with  10  of  oxygen,  therefore  the 
formula  of  the  compound  is  C2O. 

1  Phil.  Trans,  for  1814,  i  et  seq. 

2  Wollaston  appears  to  have  first  used  this  term  in  1808  (Phil.  Trans.}. 

3  See  Cannizzaro,  C.  S.  Journal  [2],  10.  945. 


§  7]  ATOMS   AND   MOLECULES.  I  5 

It  seemed  impossible  to  determine  the  equivalent  weight 
of  carbon,  just  as  in  Dalton's  system  it  was  impossible  to 
determine  the  atomic  weight  of  carbon1. 

If  the  unit  of  equivalency  is  8  parts  by  weight  of  oxygen, 
what  is  the  equivalent  of  copper?  An  electric  current  is 
passed  through  a  voltameter  and  also  through  molten  cuprous 
chloride ;  for  every  8  parts  by  weight  of  oxygen  set  free 
in  the  voltameter  63*5  parts  by  weight  of  copper  appear  in 
the  second  vessel :  cupric  chloride  is  substituted  for  cuprous 
chloride,  and  now  3175  parts  of  copper  are  eliminated  for 
every  8  parts  of  oxygen.  So  in  the  compounds  of  copper 
and  oxygen,  we  have  in  one  case  63-5  of  copper  combined 
with  8  of  oxygen,  in  the  other  3175  of  copper  with  8  of 
oxygen. 

So  long  as  the  term  equivalent  was  applied  to  acids  and 
bases,  or  to  oxides,  it  had  a  definite  meaning.  The  amount 
of  oxide  which  neutralised  unit  weight  of  standard  acid  was 
the  equivalent  of  that  oxide,  because  it  was  equal,  so  far  as 
neutralising  power  went,  to  some  other  weight  of  another  oxide. 
'  When  we  speak  of  the  equivalent  of  a  body,'  said  Gerhardt, 
'  we  should  always  indicate  to  what  other  body,  to  what  func- 
'tions,to  what  properties,that  equivalent  corresponds2/  Richter 
shewed  that  there  is  a  constant  relation  between  the  amount 
of  oxygen  in  an  oxide  and  that  in  the  acid  which  neutralises 
this  oxide :  e.g.,  in  sulphuric  acid,  he  said,  the  oxygen  is  three 
times,  and  in  nitric  acid  five  times  that  in  the  oxide  neu- 
tralised, &c.  This  rule  was  made  general.  Now  the  equiva- 
lent of  aluminium  was  said  to  be  137:  the  formula  of 
sodium  sulphate,  in  accordance  with  Richter's  rule,  was  written 
NaO.SO8;  hence  the  formula  of  aluminium  sulphate  should 
have  been  written  AUO.SO3,  (137  x  f  =  amount  of  alumi- 
nium uniting  with  8  parts  by  weight  of  oxygen);  but  the 
formula  was  almost  invariably  written  A12O3 .  3SO3,  which  is 
a  departure  from  a  strictly  equivalent  notation. 

1  Thus   for    iron    we   have    the   equivalents    28   and   i8'6 :    for  carbon,  the 
equivalents  3,  4,  8,  and  12:    for  nitrogen,  4*6  and  2'3  :    for  oxygen,  8  and  16: 
for  silicon,  7  and  3-5,  &c.  &c.     Williamson,  C.  S.  Journal,  22.  328. 

2  Quoted  by  J.  J.  Griffin  in  the  The  Radical  Theory  in  Chemistry,  p.  32. 


1 6  CHEMICAL  STATICS.  [§  8 

Mohr  (Mechanische  Theorie  der  Chemise/ten  Affinitdt)  who 
strongly  upheld  an  equivalent  notation,  admits  (loc.  cit.  pp.  143 
— 144)  that  no  equivalency  exists  between  the  oxides  RO 
and  R2O3 ;  he  also  despairs  of  determining  the  equivalent  of 
phosphoric  acid.  Those  quantities  of  two  substances  are,  he 
says,  equivalent,  which,  by  combination  with  other  bodies, 
produce  similar  compounds  ;  but  he  fails  to  define  '  similar 
'  compounds,'  or  rather  he  admits  the  impossibility  of  such  a 
definition. 

That  the  weights  of  elements  which  mutually  combine 
do  not  always  represent  equivalent  quantities  of  these  ele- 
ments was  gradually  discovered ;  but  the  so-called  equivalent 
notation  assumed  that  these  weights  do  represent  equivalent 
quantities  of  the  combining  elements. 

8.  The  systems  of  chemical  notation  founded  respectively 
on  the  atomic  weights  of  Dalton,  and  on  the  equivalents  of 
Wollaston  continued  to  hold  divided  sway  over  the  minds  of 
chemists  *.  A  man  of  preeminent  powers  of  classification  was 
required. 

The  system  of  chemical  classification  and  notation  elabo- 
rated by  JACOB  BERZELIUS  (1779—1848)  was  essentially 
electrical.  The  dualism  of  the  Berzelian  school  was  the  logical 
development  of  the  views  of  Lavoisier  concerning  salts,  and  of 
the  hypothesis  of  Davy  upon  the  relations  between  electrical  and 
chemical  actions 2.  At  present,  however,  this  part  of  the  work 
of  the  great  Swedish  chemist  does  not  specially  concern  us. 

Berzelius  recognised  the  necessity  of  extending  the  general- 
isations already  made  concerning  the  combinations  of  atoms. 
To  say  that  when  two  elements,  by  combining  together,  form 
only  one  compound,  that  compound  contains  one  atom  of  each 

1  The  student  who  wishes  to  pursue  this  subject  in  greater  detail  may  consult 
any  of  the  older  text-books,  on  the  laws  of  combination  and  atomic  weights,  e.g. 
Turner's  Chemistry •,  pp.  212 — 235  ;  he  will  thus  become  persuaded  how  impossible 
it  was  to  determine  the  values  of  atomic  weights  with  certainty.     Some  interesting 
points   especially   regarding    the   proposal   to   give  two   equivalents,   or  atomic 
weights,    to   some  of  the   elements  will  be  found  in  Griffin's  Radical  Theory, 
pp.  30—43. 

2  For  a  brief  notice  of  the  system  of  Berzelius  regarding  the  constitution  of 
compounds  see  chap.  n.  pp.  108 — in. 


§  8]  ATOMS  AND   MOLECULES.  I/ 

element,  was,  according  to  Berzelius,  not  fully  warranted  by 
facts. 

To  discover  the  laws  which  govern  atomic  combinations 
was  the  task  that  Berzelius  proposed  to  himself.  He  argued 
that  inasmuch  as  the  number  of  compounds  formed  by  the 
mutual  actions  of  any  two  or  three  elements  is  evidently  very 
limited,  there  must  be  certain  laws  expressing  the  conditions 
under  which  alone  atoms  combine. 

Berzelius  regarded  Gay  Lussac's  law  of  gaseous  combi- 
nation— 'equal  volumes  contain  equal  numbers  of  atoms' — 
as  the  most  important  of  the  generalisations  made  concerning 
atomic  combinations,  but  he  restricted  the  application  of  this 
law  to  elementary  gases.  He  admitted  that  a  compound  gas 
might  contain  half,  or  even  less  than  half  as  many  atoms  as 
were  present  in  an  equal  volume  of  an  elementary  gas,  he 
did  not  compare  the  atomic  composition  of  elementary  and 
compound  gases  ;  he  thus  evaded  the  objections  urged  by 
Dalton  against  the  law  of  Gay  Lussac,  and  at  the  same 
time  he  declined  to  accept  the  statement  of  Avogadro, 
'  equal  volumes  contain  equal  numbers  of  molecules! 

The  ratios  of  the  weights  of  the  combining  volumes  of 
elementary  gases  were  regarded  by  Berzelius  as  representing 
the  ratios  of  the  weights  of  the  atoms  of  those  elements ;  there- 
fore to  water,  nitric  oxide,  and  ammonia  he  gave  the  formulae, 
H2O.  NO,  and  NH3  because  two  volumes  of  hydrogen  unite 
with  one  volume  of  oxygen  to  form  water,  one  volume  of 
nitrogen  unites  with  one  volume  of  oxygen  to  form  nitric 
oxide,  and  ammonia  is  produced  by  the  union'  of  one  volume 
of  nitrogen  with  three  volumes  of  hydrogen. 

But  the  volumetric  method  was  of  limited  application  to 
the  problems  of  chemical  synthesis.  Berzelius  attempted  to 
state  general  rules  with  regard  to  the  combinations  of  atoms 
in  solid  and  liquid  compounds.  These  rules  referred  chiefly 
to  oxygen  compounds  which  play  so  important  a  part  in 
mineral  chemistry  wherewith  Berzelius  largely  concerned  him- 
self. The  most  important  of  the  Berzelian  rules  were  three. 

I.  If  an  element  form  two  oxides  with  twice  as  much 
oxygen  by  weight  in  one  as  in  the  other,  that  with  the 
M.  c.  2 


1 8  CHEMICAL   STATICS.  [§  8 

smaller  amount  of  oxygen  is  to  be  represented  as  a  compound 
of  one  atom  of  element  united  with  one  atom  of  oxygen,  and 
that  with  the  larger  quantity  of  oxygen  as  one  atom  of 
element  combined  with  two  atoms  of  oxygen. 

II.  If  an  element  form  two  oxides,  one  of  which  contains 
one  and  a  half  times  as  much  oxygen  as  the  other,  that  with 
the  less  oxygen  is  to  be  represented  as  composed  of  one  atom 
of  element  and  one  atom  of  oxygen,  and  the  other  compound 
as  formed  by  the  union  of  two  atoms  of  element  with  three 
atoms  of  oxygen. 

III.  The   amount   of   oxygen    in    an    acid    is   a   simple 
multiple  of  the  amount  of  oxygen  in  any  base  with  which  the 
acid  combines1,  and  this  multiple  generally  also  expresses  the 
number  of  atoms  of  oxygen  in  the  acid :  thus  in  the  case  of 
sulphuric  acid  and  potash,  an  amount  of  acid  containing  24 
parts  by  weight  of  oxygen  combines  with  that  amount  of 
potash  which  contains  8  parts  of  oxygen,  therefore,  by  the 
Berzelian  rule,  there  are  three  atoms  of  oxygen  in  one  atom 
of  sulphuric  acid.     When  nitric  acid  neutralises  potash  there 
are  40  parts    of  oxygen  in   the  acid  for  every   8  parts  in 
the   base;    therefore   an   atom    of    nitric   acid    contains   five 
atoms  of  oxygen. 

By  the  use  of  these  rules  Berzelius  determined  the  for- 
mulae of  many  metallic  oxides  and  salts.  While  he  was  thus 
engaged,  Dulong  and  Petit2  announced  their  'law  of  atomic 
'heats';  and  shortly  afterwards  Mitscherlich 3,  his  'law  of 
'  isomorphism.' 

Berzelius  adopted  both  laws,  and  by  their  help4,  along 
with  his  own  rules,  he  drew  up  a  table  of  atomic  weights 
which  in  very  many  cases  were  almost  identical  with  those 
now  in  general  use. 


1  This  had  been  stated  by  Richter  many  years  before  Berzelius  :  see  ante  p.  15. 

2  See  p.  46.  3  See  pp.  65—71. 

4  Berzelius  formulated  the  law  of  isomorphism  in  its  bearing  on  the  problem  of 
determining  atomic  weights,  thus  (Lehrbuch  3rd  ed.,  p.  98) — when  one  body  is 
isomorphous  with  another,  the  number  of  atoms  in  which  is  known,  then  the 
number  of  atoms  in  the  other  is  known  also,  because  isomorphism  is  a  mechanical 
consequence  of  identity  of  atomic  structure. 


§  9]  ATOMS  AND   MOLECULES.  19 

TABLE  OF  ATOMIC  WEIGHTS.    BERZELius1. 

Arsenic         75'33  Manganese  57'Q2  Silver         2i6'6i 

Calcium        41*03  Sodium  46-62  Silicon         44 '47 

Chlorine       35 '47  Phosphorus  31 '43  Nitrogen      14-18 

Iron               54'36  Mercury  2O2'86 

Iodine  123*2  Oxygen  i6'oo  Hydrogen    =  I. 

Carbon          12*25  Sulphur  32*24 

Berzelius  himself  admits  that  the  atomic  weights  deter- 
mined by  his  rules  are  in  many  cases  open  to  doubt  (LeJirbucJi 
1st  edition,  vol.  III.  part  i.  pp.  87 — 102).  Berzelius  had  a 
remarkable  amount  of  tact ;  his  rules  were  empirical  but  he 
balanced  probabilities  so  well  that  he  generally  got  the  best 
possible  result. 

9.  The  separation  which  Berzelius  made  between  formulae 
of  elementary  and  compound  bodies,  and  his  refusal  to 
accept  Avogadro's  hypothesis  while  admitting  Gay  Lussac's 
generalisation,  led  him  to  a  very  curious  result. 

Two  volumes  of  hydrogen,  weighing  2,  combine  with  one 
volume  of  oxygen,  weighing  16,  to  form  two  volumes  of 
water-gas.  Therefore  said  Berzelius,  two  atoms  of  hydro- 
gen combine  with  one  atom  of  oxygen  to  form  one  atom  of 
water-gas.  But  water  contains  less  oxygen,  relatively  to 
hydrogen,  than  any  other  known  oxide  of  hydrogen,  therefore 
it  is  better  to  regard  it  as  a  compound  of  one  atom  of  oxygen 
with  one  double  atom,  or  with  one  atom  itself  composed  of  two 
equivalents,  of  hydrogen.  Again  in  the  formation  of  the 
lowest  oxide  of  nitrogen  two  volumes  of  nitrogen  combine 
with  one  of  oxygen  ;  but  it  is  better  to  regard  the  nitrogen 
as  composed  of  double  atoms  each  occupying  twice  the 
volume  of  the  atom  of  oxygen.  Once  more ;  hydrogen  and 
chlorine  combine  in  equal  volumes,  and  the  volume  of  the 
product — hydrochloric  acid — is  equal  to  the  sum  of  the 
volumes  of  its  constituents ;  but  as  the  hydrogen  atom  was 
regarded  by  Berzelius  as  double,  he  wrote  the  atomic  syn- 
thesis of  hydrochloric  acid  as 

H2  +  C1.2  =  H2C12. 

2  vols.  2  vols.     4  vols. 

1  Jahresberichte,  1828.  73. 

2 — 2 


20  CHEMICAL   STATICS.  [§  IO 

These  results  are  evidently  to  be  traced  to  the  failure  of 
Berzelius  clearly  to  distinguish  atom  from  equivalent,  and  to 
his  refusal  fully  to  accept  the  distinction  between  atom  and 
molecule  enunciated  by  Avogadro1. 

To  the  great  French  chemists,  DUMAS,  GERHARDT  and 
LAURENT,  is  chiefly  due  the  introduction  into  general  use  of 
a  system  founded  on  Avogadro's  distinction  between  atoms 
and  molecules. 

10.  Dumas  early  accepted  Avogadro's  hypothesis  ;  from 
the  specific  gravities  of  gases  he  deduced  the  relative  weights 
of  the  molecules  of  these  gases  :  in  order  to  gain  more  informa- 
tion regarding  molecular  weights  he  introduced  a  new  method 
for  finding  the  specific  gravities  of  gases.  By  this  method  he 
determined  the  molecular  weight  of  sulphur  to  be  96,  and 
that  of  phosphorus  to  be  124;  but  from  the  analogy  of 
sulphur  compounds  with  those  of  oxygen,  from  various 
chemical  considerations  regarding  phosphorus  compounds, 
and,  I  think  we  must  add,  from  not  keeping  Avogadro's 
statement  quite  distinct  from  that  of  Gay  Lussac,  Dumas 
convinced  himself  that  these  results  were  incorrect.  The 
molecular  weight  of  mercury  also  seemed  to  be  abnormal. 
Dumas  knew  of  exceptions  to  the  law  of  Dulong  and  Petit. 
Mitscherlich's  law  of  isomorphism  remained;  but  Mitscherlich 
had  himself  shewn  that  the  same  compound  might  assume 
more  than  one  crystalline  form,  how  then  could  trustworthy 
conclusions  regarding  atomic  structure  be  deduced  from  so 
vague  a  law  ?  Dumas,  and  indeed  chemists  generally,  began 
to  despair  of  the  whole  theory  of  atoms ;  they  tried  to  find 
relief  in  equivalents,  so  called,  and  in  spite  of  the  many 
difficulties  they  gradually  tended  towards  an  equivalent 
notation,  a  notation  which  nevertheless  they  could  not  make 
thoroughly  self-consistent,  but  which  seemed  to  involve  fewer 
hypotheses  than  that  founded  on  the  theory  of  atoms2. 

L.  Gmelin  even  regarded  the  law  of  fixity  of  composition 

1  For  a  more  detailed  account  of  the  work  of  Berzelius  on  atomic  weights  see 
Ladenburg's  Entw ickelungsgeschichle  der  Chemic,  pp,  89 — 100. 

2  For  a  general  account  of  Dumas'  influence  on  chemical  theories  see  his 

stir  la  Philosophic  Chimique,  republished  in  1878. 


§  II]  ATOMS   AND   MOLECULES.  21 

as  only  true  under  special  conditions.  When  the  affinity 
between  two  bodies  is  small,  they  may  be  united,  said  Gmelin, 
in  almost  any  proportions,  when  the  affinity  is  large  they 
tend  to  combine  in  fixed  proportions.  A  number  may  be 
given  to  each  element  representing  the  relative  amount  of 
that  element  which  combines  with  other  elements  to  form 
stable  and  well-marked  compounds;  this  'combining  weight' 
may  be  called  '  atomic  weight,'  but  it  is  only  a  number. 
Gmelin  adopted  8  as  the  combining  weight  of  oxygen,  6  as 
that  of  carbon  &c. :  the  formula  of  water  on  his  system  again 
became  HO. 

This  notation  was  at  best  a  compromise,  and  unsatis- 
factory, but  it  was  very  generally  adopted  for  many  years. 

Inorganic  chemistry  had  failed  to  introduce  an  accurate 
and  satisfactory  theory  of  chemical  structure  :  it  was  now  the 
turn  of  organic  chemistry  to  attempt  the  task. 

ii.  Among  the  most  ardent  followers  of  the  new  chem- 
istry introduced  by  Dumas,  were  two  men,  whose  names  are 
ever  to  be  associated  as  those  of  a  brilliant  pair  of  students  of 
nature  who  died  all  too  early  for  the  work  which  seemed  given 
them  to  do.  Gerhardt  and  Laurent  occupy  a  prominent 
place  among  the  modern  reformers  of  chemistry ;  they  intro- 
duced order  into  chemical  notation,  and  system,  where  system 
had  been  conspicuous  by  its  absence1. 

In  criticising  the  system  of  so-called  equivalent  weights 
Gerhardt  adopted  the  only  true  method,  he  studied  actually 
occurring  chemical  reactions. 

In  a  number  of  reactions  between  compounds  of  carbon 
in  which  carbon  dioxide,  water,  and  ammonia  were  produced, 
Gerhardt2  found  that  when  so-called  equivalent  weights  of 
the  reacting  bodies  were  employed,  the  quantities  of  these  three 
compounds  evolved  could  always  be  represented  by  whole 
multiples  of  the  formulae  C2O4,  H2O2,  and  NH3  respectively, 
(C  =  6,  N=i4,  O  =  8). 

1  Laurent's  Chemical  Method  [Cavendish  Society  Publications]  gives  a  general 
account  of  the  more  important  work  of  these  chemists. 

2  J'  fur  pract.   Chemie,  27.  439;   and  Ann.  Chim.  Phys.  [3]  7.  129:  and  8. 
238. 


22  CHEMICAL   STATICS.  [§  II 

He  therefore  concluded  that  these  formulae,  rather  than 
the  commonly  accepted  formulae  CO2,  HO  (and  NH3),  must 
represent  equivalent  weights  of  the  compounds  in  question. 

Similarly  he  concluded  that  the  equivalent  formulae  of 
sulphur  dioxide  and  carbon  monoxide  must  be  S2O4  and 
C2O2  respectively :  and  arguing  from  these  conclusions  he 
thought  himself  justified  in  saying  that  the  true  equivalents 
of  carbon,  sulphur  and  oxygen  are  12,  32,  and  16,  and 
not  6,  1 6,  and  8  as  generally  adopted.  Gerhardt  likewise 
applied  his  acute  reasoning  powers  to  an  examination  of  the 
arguments  which  determined  Berzelius  and  others  to  adopt 
formulae  representing  weights  of  four  volumes  of  many  carbon 
compounds  ;  these  arguments  he  proved  to  be  fallacious. 

Laurent  examined  the  groundwork  on  which  the  systems 
of  equivalent  and  atomic  notation  were  based.  His  methods 
of  reasoning  were  founded  on  experimentally  determined 
facts,  hence  their  irresistible  force. 

If  formulae  are  to  represent  equivalent  weights  of  sub- 
stances, then  said  Laurent,  a  standard  must  be  adopted. 
But  it  had  been  frequently  shewn  that  the  quantities  re- 
presented by  so-called  combining  weights  were  not  always 
mutually  equivalent.  Power  of  neutralising  unit  weight  of 
standard  substance  might  be  adopted  as  the  reaction  on 
which  to  base  the  system,  but  this  method  could  be  applied 
only  to  a  limited  number  of  substances. 

The  idea  of  equivalency  is  associated  with  function  ;  What 
is  a  given  substance  capable  of  doing  ? :  this  question  must 
be  answered  before  the  equivalent  of  the  substance  can  be 
determined.  But  in  one  action  certain  weights  of  two  bodies 
may  be  equivalent,  while  altogether  different  weights  of  the 
same  bodies  are  equivalent  in  another  reaction. 

Laurent  affirmed  that  it  was  possible  to  found  a  systematic 
.notation  on  equivalent  weights  assigned  to  the  elements. 
Thus,  in  ferrous  oxide  28  parts  by  weight  of  iron  are  combined 
with  8  parts  by  weight  of  oxygen, — let  Fe  =  28,  then  ferrous 
sulphate  is  represented  by  the  formula  Fe2SO4;  but  in  ferric 
oxide  there  are  2 .  -^8-  (i.e.  1 8'6)  parts  by  weight  of  iron  for 
every  8  parts  by  weight  of  oxygen, — let  f e  =  186,  then  the 


§  II]  ATOMS   AND   MOLECULES.  23 

formula  for  ferric  sulphate  is  fe2  SO4 :  the  formulae  Fe2  SO4 
and  fe2  SO4  represent  strictly  equivalent  quantities  of  the  two 
sulphates  of  iron.  So  also  if  the  composition  of  potassium- 
hydrogen  sulphate  is  expressed  by  the  formula  KHSO4,  then, 
in  a  system  of  notation  founded  on  equivalent  weights,  the 
composition  of  the  double  sulphate  of  potassium  and  alu- 
minium is  represented  by  the  formula  K!  Al|  SO4  (Al  =  27*3). 
But  such  a  notation  is  inconvenient,  and  it  frequently 
conceals  most  important  facts ;  e.g.  in  a  strictly  equivalent 
notation  the  differences  between  monobasic  and  polybasic 
acids  disappear. 

Laurent  returned  to  the  generalisation  of  Avogadro  and 
made  that  the  basis  of  his  system  ;  he  clearly  distinguished 
between  molecules  and  atoms,  and  he  applied  the  law  of  equal 
volumes  and  equal  numbers  to  molecules  only.  He  admitted 
that  apparent  exceptions  to  the  Avogadrean  law  existed — 
e.g.  the  molecules  of  sulphuric  acid  and  salammoniac  vapour 
appeared  to  occupy  twice  the  volume  occupied  by  the 
molecule  of  hydrogen  ; — but  he  said  that  this  hypothesis 
generalised  the  facts  better  than  any  other  which  had  been 
proposed. 

Laurent  founded  his  system  on  an  atomic  basis,  and  a  fun- 
damental point  was  the  distinction  between  atom  and  molecule. 
He  adopted  formulae  representing  two  volumes :  the  facts 
of  '  nascent '  action  he  explained  by  the  conception  of  atoms 
as  distinct  from  molecules.  Molecule  he  defined  to  be  '  the 
*  amount  of  a  gaseous  substance  which  occupies  twice  the 
'  volume  occupied  by  an  atom  of  hydrogen,'  or,  '  the  smallest 
'  amount  of  a  substance  capable  of  taking  part  in  a  chemical 
'  reaction.'  Atom  he  defined  as  '  the  smallest  amount  of  an 
'  element  which  enters  into  the  composition  of  a  compound.' 
Here  we  have  the  application  of  the  term  molecule  to 
elements  and  compounds  alike,  while  atom  is  used  of  elements 
only. 

Equivalents  are  the  amounts  of  bodies  which  are  of  equal 
value  in  performing  a  stated  action. 

Gerhardt  and  Laurent  adopted  the  laws  of  atomic  heat 
and  isomorphism  as  aids  in  determinations  of  atomic  weights. 


24  CHEMICAL  STATICS.  [§§  12,  13 

12.  Chemical  evidence  in  favour  of  the  division  of 
elementary  molecules  during  chemical  changes  was  accumu- 
lated by  Brodie,  Wurtz,  Williamson  and  others,  but  the  work 
of  these  chemists  will  be  referred  to  in  more  detail  when  we 
come  to  speak  of  the  chemical  methods  for  determining 
molecular  weights  (see  pp.  72 — 77). 

Thus,  at  last,  we  have  arrived  at  a  clear  separation  between 
the  meanings  of  the  terms  atom,  molecule,  equivalent. 

The  system  now  adopted  in  chemistry  is  essentially  that 
of  Gerhardt  and  Laurent ;  it  is  founded  on  the  conception  of 
atoms  and  molecules.  Dalton's  fundamental  idea  has  been 
amply  confirmed  by  modern  research.  We  have  maintained 
the  idea  of  equivalency,  but  we  no  longer  speak,  as  Wollaston 
did,  of  the  equivalent  of  an  element ;  we  compare  the 
elementary  atoms  among  themselves  and  arrange  them  in 
groups  all  the  members  of  each  of  which  are  equivalent  in 
respect  of  a  certain  definite  action  they  are  capable  of  per- 
forming. 

A  true  and  fundamental  conception  once  gained  in  science 
is  never  lost,  it  may  be  largely  modified,  it  may  even  appear 
at  times  to  be  abandoned,  but  it  develops  slowly  and  bears 
much  fruit  at  last. 

The  vicissitudes  in  the  fortunes  of  a  truly  scientific  idea  are 
aptly  illustrated  by  the  history  of  the  atomic  theory.  After  a 
period  of  dormancy  of  more  than  2000  years,  the  atomic 
theory  was  revived  and  rendered  definite  by  Dalton,  was 
firmly  established  on  an  experimental  basis  by  Berzelius,  was 
almost  abandoned  by  the  school  founded  by  the  same 
chemist,  was  rehabilitated  and  again  nearly  despaired  of  by 
Dumas,  was  largely  advanced  by  Avogadro,  was  subdivided 
and  its  parts  clearly  distinguished  by  Gerhardt  and  Laurent, 
and  is  now  the  foundation-stone  of  a  great  and  ever-increasing 
edifice. 

13.  Thus  far  I  have  dealt  with  the  development  of  the 
atomic  and  molecular  theory  regarded  almost  entirely  from  the 
chemical  point  of  view.  So  great  however  is  the  importance 
of  clearly  perceiving  the  position  which  this  theory  occupies 
in  modern  chemistry,  and  of  realising  the  nature  of  the 


§  13]  ATOMS  AND   MOLECULES.  2$ 

physical  evidence  on  which,  in  its  more  recent  development, 
the  theory  so  largely  rests,  that  I  must  endeavour  very  briefly 
to  give  a  sketch  of  that  evidence,  remembering  always  that  it 
is  as  chemists,  not  as  physicists,  that  we  are  interested  in 
this  subject. 

There  are  two  general  theories  of  the  structure  of  material 
substances  :  one  assumes  that  apparently  homogeneous  bodies 
are  really  homogeneous  throughout — a  theory  which  is  in- 
capable of  explaining  the  observed  properties  of  matter — 
and  the  other,  that  apparently  homogeneous  bodies  are 
possessed  of  a  grained  structure. 

Viewed  from  a  distance,  a  brick  wall,  or  a  body  of  soldiers, 
appears  to  be  one  reddish-coloured  homogeneous  mass,  but  a 
nearer  observer  sees  that  the  wall  is  made  up  of  distinct  parts, 
that  the  company  is  composed  of  individual  men. 

The  molecular  theory  supposes  that  were  our  senses 
sufficiently  acute,  we  should  see  the  grains  or  particles  of 
which  an  apparently  homogeneous  mass  of  matter  is  composed. 

The  theory  begins  by  assuming  that  any  material  body 
'  is  made  up  of  parts  (each  of  which  is  capable  of  motion) 
'  and  that  these  parts  act  on  each  other  in  a  manner  consistent 
4  with  the  principle  of  the  conservation  of  energy1.'  These 
parts  are  called  molecules  ;  the  dynamical  definition  of  a 
gaseous  molecule  is  '  That  minute  portion  of  a  substance 
'  which  moves  about  as  a  whole,  so  that  its  parts,  if  it  has  any, 
'  do  not  part  company  during  the  motion  of  agitation  of  the 
'gas"'. 

This  definition  is  entirely  independent  of  chemical  facts. 

All  the  molecules  of  one  element  are  of  the  same  mass, 
else  differences  would  be  observed  in  the  properties  of  an 
elementary  gas,  e.  g.  hydrogen,  such  differences  arising  from 
the  separation  of  the  gas  into  portions  each  more  or  less  unlike 
the  others. 

The  relations  between  the  motions  and  the  space  occupied 
by  these  little  parts,  assuming  their  existence  and  mutual 
independence,  may  be  dynamically  deduced  by  the  aid  of  a 

1  Clerk  Maxwell,  Article  'Atom'  in  EncycL  Britannica.     (pth  Ed.) 

2  Ibid. 


26  CHEMICAL   STATICS.  [§  13 

theorem  of  Clausius,  and,  with  a  justifiable  assumption  as  to  the 
dynamical  meaning  of  temperature,  the  equation  thus  arrived 
at  expresses  with  considerable  accuracy  the  relations  actually 
existing  between  temperature  and  pressure,  and  volume,  in 
the  case  of  rarefied  gases ;  the  equation  that  is  to  say  expresses 
the  laws  of  Charles  and  of  Boyle.  When  the  gas  is  more 
condensed  the  equation  ceases  to  express  the  relations 
existing  between  temperature  and  pressure,  and  volume ; 
hence  the  theory  asserts  the  existence  in  such  a  gas  of  mutual 
attractions  or  repulsions  between  the  little  parts,  or  mole- 
cules, it  asserts  that  these  parts  are  no  longer  mutually 
independent. 

'  The  hypothesis  that  a  gas  consists  of  molecules  in  motion 
1  which  act  on  each  other  only  when  they  come  together 
'during  an  encounter,  but  which  during  the  intervals  between 
'  their  encounters — which  constitute  the  greater  part  of  their 
'  existence — are  describing  free  paths,  and  are  not  acted  on  by 
'any  molecular  forces1/  having  been  justified  by  dynamical 
reasoning,  the  next  step  is  made  by  investigating  mathemati- 
cally the  properties  of  such  a  system  of  molecules.  And  one 
deduction  thus  made  is  '  If  equal  volumes  of  two  gases  are 

*  at  equal  temperatures  and  pressures,  the  number  of  molecules 
*in  each  is   the  same,  and  therefore  the    masses  of  the  two 

*  kinds  of  molecules  are  in  tJie  same  ratio  as  the  densities  of  tJie 
'  gases  to  which  they  belong* '. 

This  statement  is  of  paramount  importance  to  the  chemist, 
inasmuch  as  on  it  is  based  his  system  of  molecular  weights. 
It  is  very  necessary  to  bear  in  mind  that  this  proposition  is 
deduced  by  dynamical  reasoning  from  a  simple  hypothesis  as 
to  the  structure  of  matter,  itself  justified  by  many  facts. 

By  analogous  reasoning,  various  deductions  are  made 
from  the  theory,  which  express  generalisations  of  experi- 
mentally determined  facts  concerning  gaseous  phenomena3. 

Passing  to  more  complex  occurrences,  the  molecular  theory 

1  Clerk  Maxwell,  Article  '  Atom '  in  Encycl.  Brit. 

2  Ibid. 

3  For  some  of  the  most  important  of  these  see  Clerk  Maxwell's   Theory  of 
Heat,  pp.  307 — 372  (6th  edition). 


§  13]  ATOMS  AND    MOLECULES.  2/ 

gives  a  simple  explanation  of  the  diffusion  of  matter,  diffusion 
of  motion,  and  diffusion  of  heat  in  gases  ;  these  phenomena 
being  regarded  by  the  theory  as  dependent  on  the  frequency 
of  the  molecular  encounters,  and  on  the  nature  of  the  actions 
between  the  encountering  molecules. 

The  molecular  theory  has  also  been  successfully  applied 
to  explain,  broadly,  many  of  the  phenomena  of  evaporation, 
condensation,  electrolysis,  and  spectroscopy. 

To  explain  spectroscopic  phenomena  it  is  apparently 
necessary  to  assume  molecules  to  be  elastic  substances,  but 
elasticity  is  just  the  property  of  matter  to  explain  which  the 
molecular  hypothesis  was  first  assumed.  The  theory  of 
1  vortex  atoms/  developed  by  Sir  William  Thomson  from  the 
original  conception  of  Helmholtz,  explains  spectroscopic 
facts — and  generally  those  facts  which  must  be  explained  by 
a  successful  molecular  theory — better  than  any  other  which 
has  yet  been  suggested.  A  short  account  of  this  theory  will 
be  found  in  the  article  'Atom'  in  the  last  edition  of  the 
Encyclopaedia  Britannica,  where  we  read  *  The  success  of  this 
'theory  in  explaining  phenomena  does  not  depend  on  the 
'ingenuity  with  which  its  contrivers  "save  appearances"  by 
'  introducing  first  one  hypothetical  force  and  then  another. 
'  When  the  vortex  atom  is  once  set  in  motion  all  its  properties 
'  are  absolutely  fixed,  and  determined  by  the  laws  of  motion  of 
1  the  primitive  fluid  which  are  fully  expressed  in  the  funda- 
'  mental  equation.' 

Attempts  have  been  made  to  determine  the  absolute  size 
of  molecules1,  and  although  the  results  must  be  regarded  as 
but  rough  estimates,  nevertheless  they  shew  that  to  measure 
molecules  is  a  legitimate  object  of  scientific  investigation. 
The  smallest  portion  of  matter  visible  by  the  help  of  a  good 
microscope  may  be  taken  to  be  a  cube  each  side  of  which 
measures  4oVotn  of  a  millimetre  in  length ;  such  a  cube  will 
contain — according  to  the  rough  measurements  hitherto 
made — from  60  to  100  millions  of  molecules2. 

1  See  especially  Sir  W.  Thomson,  Nature  1.  p.  551,  and  also  28.  pp.  203, 
250,  274. 

2  Clerk  Maxwell,  he.  cit. 


28  CHEMICAL   STATICS.  [§  13 

The  foundations  of  a  truly  mathematical  theory  have  been 
laid  by  Helmholtz  and  Thomson  in  their  theory  of  vortex 
atoms;  but,  apart  from  this,  the  fact  that  the  proposition 
commonly  known  as  Avogadro's  law  may  be  deduced  by 
dynamical  reasoning  from  a  simple  hypothesis  which  ad- 
mits, although  as  yet  only  to  a  limited  extent,  of  the  ap- 
plication of  mathematical  methods,  and  which  is  justified  by 
a  large  number  of  physical  facts,  suffices  to  make  that  law  of 
extreme  importance. 

Mathematical  theories  of  physical  phenomena  in  which 
the  forces  at  work  are  thoroughly  known,  are  complete,  and 
are  capable  of  making  predictions  which  may  afterwards  be 
verified  by  experiment,  or  even  of  predicting  phenomena 
which  are  altogether  beyond  the  reach  of  experimental  veri- 
fication. When  however  the  forces  are  but  partly  known,  the 
theory  may  predict  results  but  cannot  give  a  complete  ac- 
count of  the  phenomena  to  which  it  is  applied1.  Now,  we 
know  very  little  of  the  forces  at  work  in  the  phenomena  called 
chemical,  hence  a  mathematical  theory  of  chemical  action 
cannot  as  yet  be  formed.  A  beginning  has  been  made  in  the 
knowledge  of  molecular  forces,  but  until  our  knowledge  is 
much  extended,  until  we  can  generalise  the  conditions  of 
molecular  actions  and  reactions,  and  also  of  molecular  de- 
compositions and  recompositions,  we  cannot  expect  to  gain  a 
complete  mathematical  theory  of  chemical  action.  At  present 
we  can  use  the  molecular  theory  of  matter  only  in  a  most 
general  form,  trying  to  make  our  deductions  therefrom  as 
accurate  as  possible,  and  always  testing  these  deductions  by 
experiment. 

Attempts  have  recently  been  made  to  apply  a  more 
strictly  dynamical  method  of  reasoning  than  is  presented  by 
the  molecular  theory,  to  certain  chemical  phenomena  ;  these 
will  be  referred  to  under  the  second  main  division  of  this  book. 

An  atomic  theory  has  been  elaborated  by  the  chemist ;  a 
molecular  theory  of  matter  has  been  propounded  by  the 
physicist,  and  has  been  advanced  so  far  as  to  allow  of  wide 
conclusions  being  deduced  therefrom  by  strictly  dynamical 

1  See  Thomson  and  Tait,  Treatise  on  Natural  Philosophy ',  1.  p.  445. 


§  14]  ATOMS  AND   MOLECULES.  29 

reasoning ;  no  theory  asserting  the  continuity  of  matter  has 
been  found  capable  of  explaining  the  observed  phenomena  of 
matter ;  hence  to  accept  the  molecular  theory,  as,  at  present, 
the  only  feasible  working  hypothesis,  is  simply  to  obey  the 
dictates  of  the  scientific  method. 

14.     Equal  volumes  of  gases  contain  equal  numbers  of 

molecules. 

Let  us  now  consider  one  or  two  chemical  reactions  between 
gaseous  substances. 

Hydrogen  combines  with  chlorine  to  form  hydrochloric  acid. 
2  vols.  „  2  vols.         „          4  vols.         „ 

But  since  equal  volumes  contain  equal  numbers  of  mole- 
cules, and  since  each  molecule  of  hydrochloric  acid  contains 
both  hydrogen  and  chlorine,  it  is  evident  that  each  molecule 
of  hydrogen  by  combination  with  one  molecule  of  chlorine 
produces  not  one  but  two  molecules  of  hydrochloric  acid. 

So  again, 

Nitrogen  combines  with  hydrogen  to  form  ammonia. 
2  vols.  „  6  vols.  „        4  vols. 

Here  again  each  nitrogen  molecule  has  given  rise  to  two 
molecules  of  ammonia.  Hence  it  is  evident  that  although  the 
parts  of  a  molecule  of  hydrogen,  nitrogen,  or  chlorine  '  do  not 
'  part  company  during  the  motion  of  agitation  of  the  gas '  to 
which  the  molecule  belongs,  these  parts  nevertheless  do  part 
company  in  those  chemical  reactions  which  are  stated  above. 
When  various  reactions  between  gaseous  substances  are 
studied  this  conclusion  is  found  to  hold  good  throughout 
a  large  range  of  chemical  phenomena.  Hence  the  chemist 
is  obliged  to  recognise  a  portion  of  matter  smaller  than 
the  molecule;  this  smaller  portion  of  matter  is  the  atom1. 

In  the  above  and  in  other  reactions  it  is  shewn  that  the 
molecules  of  hydrogen,  nitrogen,  and  chlorine  split  into  two 
parts  when  these  molecules  act  chemically  on  each  other  or  on 
other  molecules ;  hence  the  molecules  of  these  elements  may  be 

1  It  is  well  to  note  that  the  molecular  theory  of  matter  as  applied  to  chemical 
phenomena  does  not  assert  or  deny  the  finite  divisibility  of  matter.  In  C.  S. 
Journal  [2],  13.  501,  there  is  a  most  interesting  paper  by  Clerk  Maxwell  on  '  The 
'dynamical  evidence  of  the  molecular  constitution  of  bodies.' 


30  ,      CHEMICAL    STATICS.  [§14 

represented  by  the  symbols  H2,  C12,  and  N2  respectively. 
These  symbols  represent  weights  of  equal  volumes  of  the 
three  elements ;  if  one  of  these  weights  be  taken  as  the  unit, 
the  other  weights  are  evidently  the  weights  of  the  molecules 
of  the  gases  in  question  referred  to  this  standard,  because 
equal  volumes  contain  equal  numbers  of  molecules,  and  there- 
fore 'the  masses  of  the  two  kinds  of  molecules  are  in  the 
'  same  ratio  as  the  densities  of  the  gases  to  which  they  belong.' 

Hydrogen  is  the  universally  adopted  standard  of  reference 
for  molecular  weights. 

The  modern  molecular  theory  of  matter  is  not  iden- 
tical with  the  atomic  theory  of  Dalton ;  it  is  based  on 
evidence  of  a  different  kind,  it  is  essentially  a  physical  and 
dynamical  theory,  although  strengthened  by  chemical  argu- 
ments. The  atomic  theory  of  modern  chemistry  may  be 
regarded  as  growing  out  of  the  application  of  reasoning 
founded  on  chemical  facts  to  the  molecular  theory  of  matter. 

Assuming  'Avogadro's  law'  and  remembering  that  the 
hydrogen  molecule  divides  into  two  parts  in  many  chemical 
changes,  we  arrive  at  the  practical  definition  of  molecular 
weight. 

The  molecular  weight  of  a  gas  is  the  weight  of  that  volume 
thereof  which  is  equal  to  the  volume  occupied  by  two  parts  by 
weight  of  hydrogen. 

In  determining  the  specific  gravity  of  a  gas  it  is  easier, 
and  less  liable  to  error,  to  find  the  weight  of  the  vessel  filled 
with  air  than  with  hydrogen ;  the  result  is  therefore  stated  as 
specific  gravity  referred  to  air  as  unity.  Now  the  specific 
gravity  of  hydrogen  is  '06926  [air=  i];  the  molecular  weight 
required  is  specific  gravity  referred  to  hydrogen  as  2,  hence 
if  M=  molecular  weight,  and  d—  specific  gravity  referred  to 

air  as  unity,  M  —  — -^ — ^=28*87.^.     Hence  the  practical  rule 
000,20 

for  determining  the  molecular  weight  of  a  gas : — 

Find  the  specific  gravity ',  i.e.  the  ratio  between  the  weights 
of  equal  volumes  of  the  gas  and  air  under  the  same  conditions 
of  temperature  and  pressure,  and  multiply  this  by  28-87. 


§15] 


ATOMS   AND    MOLECULES. 


15.     The  following  table  presents  the  results  hitherto  ob- 
tained regarding  the  molecular  weights  of  elementary  gases. 

[The  numbers  in  column  V  are  not  always   exactly  equal   to  the  products 
obtained  in  column  iv;  for  an  explanation  see  pp.  34 — 35.] 

Molecular  weights  of  elementary  Gases. 


I 

Name  of  element 

II 

Spec,  gravity 
(air=i) 

III 

Temp,  of 
observation 

IV 

(sp.  gr.) 
X  28-87 

V 

Molecular 
weight 

1  Hydrogen 

2  Nitrogen 

'06926 
0-97I3 

O° 
0° 

2 
28-04 

2 
28*02 

3  Oxygen 

no6 

about  1400° 

3^94    I 

4 

1-10563 

o° 

3I-92    J 

3    9 

5        „        (ozone) 

1-658 

— 

47-86 

47-88 

6  Sulphur 

2-23 

860° 

64-4     i 

7 

2-24 

1040° 

64-6 

63-96 

8 

u 

2-17 

about  1400° 

62-6     j 

Sa 
j) 

2-93 

665° 

84-6 

? 

9 

6-62 

524° 

191-1 

191-88 

10  Chlorine 

2-45 

200° 

7073   ] 

11 

2-61 

about  1000° 

7535    f 

70-74 

j) 

2-44 

about  1200° 

70-72   J 

12  Cadmium 

3-94 

about  1000° 

1137 

II2'I 

13  Phosphorus 
11 

4-35 
4-50 

500° 
about  1000° 

125-6     ) 
129-9     f 

I23-84 

15  Arsenic 

16 

IO'2 
10-65 

860° 
644°—  668° 

294-5 
307-4     } 

299-6 

17  Bromine 

T54 

100° 

18 

J    J^ 

5-38 

100° 

I55-3     1 

I59'5 

19 

about  1500° 

117-9 

? 

20  Selenion 

5-68 

about  1400° 

i6ri 

I57-6 

21 

6-37 

about  1000° 

183*9 

22 

7-67 

860° 

221-4 

236-4 

23  Mercury 

6-96 

about  1000° 

200-93   } 

24 
25 

6-98 
7-03 

446° 
424° 

201-5      1 
203-0      f 

199-8 

26            ',' 

67 

882° 

193*4     J 

27  Iodine 

8-8 

250°—  450° 

254-0    -i 

28 

872 

185° 

2517 

29            ", 

30 
J) 

870 
872 

447° 
about  looo 

251-2 
2517 

253-07 

31 

8-84 

250° 

255-2 

31»           ^ 

8-55 

665° 

246-8     j 

32             » 

5-87 

about  1100° 

169-4 

? 

33 

4-76 

about  1500° 

I37-4 

[?  126-53] 

34  Tellurium 

9-08 

about  1400° 

262-1 

255 

1  REGNAULT,  Compt.  rend.  20.  975.  2  Ibid.,  loc.dt.  3  V.  MEYER, 

Ber.  12.  1426.  4  REGNAULT,  loc.  cit.  5  SORET,  Compt.  rend.  61. 


32  CHEMICAL  STATICS.  [§  1 6 

The  specific  gravities  of  the  vapours  of  potassium  and  sodium  have 
been  determined  by  Dewar  and  Dittmar  (Chem.  News,  27.  121),  and  by 
Dewar  and  Scott  (id.  40.  293)  :  but  the  numbers  are  not  given  in  this 
table  because  V.  Meyer  has  shewn  that  the  process  made  use  of  was  not 
trustworthy  (Ber.  13.  391). 

1 6.  So  many  determinations  of  molecular  weights  of 
compound  gases  have  been  made  that  an  enumeration  of  all 
the  results  would  be  perplexing,  and  of  no  special  value.  The 
method  is  applicable  to  elements  and  compounds  alike.  The 
following  numbers  are  given  here  as  they  illustrate  a  point  of 
general  importance. 

Specific  gravities  of  certain  compound  gases. 


Name. 

Sp.  gr. 

Temperature. 

Phosphorus  pentachloride 

5'08 

1  80° 

„ 

4'99 

190° 

„ 

4'3° 

230° 

„ 

3-69 

290° 

5) 

3*6 

335° 

Nitrogen  tetroxide 

2-80 

29° 

„ 

2*40 

45° 

„ 

2-03 

66° 

„ 

1-83 

83° 

'* 

1-50 

151° 

941   and  64.   904.  6and7  DEVILLE  and  TROOST,  Compt.  rend.   56.   891. 

8  V.    MEYER,    Ber.    12.    1112.  8a  TROOST,    Compt.    rend.    95.    30. 

9  DUMAS,    Ann.  Chim.    Phys.   (2)  50.    170.  10  LUDWIG,  Ber.  1.    232. 
11  V.  MEYER,  Ber.  13.  400.              lla  Ibid.  do.   15.    2773    (mean   of  5   experi- 
ments).            12  DEVILLE  and  TROOST,  Compt.  rend.  49.  239.  isandi4  jbid. 
do.,  56.  891.             13  Ibid.,  loc.  cit.             16  MiTSCHERLiCH,  Annalen  12.  159. 
17  Ibid.,  loc.  cit.            is  y.  MEYER,   Ber.  13.  4o6.             19  CRAFTS,    Compt. 
rend.  90.  183.            20, 21  and 22  DEVILLE  and  TROOST,  loc.  cit.            23  V.  MEYER, 
Ber.  13.  1107  and  mo  (mean  of  6  experiments).              24  DUMAS,  Ann.   Chim. 
Phys.  (2)  33.  337.              25  MITSCHERLICH,  loc.  cit.             26  BINEAU,   Compt. 
rend.  49.    799.              27  V.   MEYER,    and  MEIER  and  CRAFTS,   Ber.   13.   868 
(mean  of  7  experiments).             «  DUMAS,  loc.  cit.             29  and  30  DEVILLE  and 
TROOST,  loc.  cit.             3l  V.  MEYER,  Ber.  13.  396.             31a  TROOST,  Compt. 
rend.  95.  30.             32  V.   MEYER,  Ber.  13.   1115.              33  Ibid.  do.  13.  1010. 
34  DEVILLE  and  TROOST,  loc.  cit. 

Note  to  preceding  table.  The  expression  '  specific  gravity  of  a  gas '  will  be 
employed  to  denote  the  specific  gravity  referred  to  air  as  unity :  the  expression 
'  vapour  density  of  a  substance '  to  denote  the  specific  gravity  of  a  substance  in  the 
gaseous  state  referred  to  hydrogen  as  unity. 


§  1 6]  ATOMS   AND   MOLECULES.  33 

Name.  Sp.  gr.  Temperature. 

Ferric  chloride  n'39  35o° 

11-37  450° 

„  iroi  620° 

Arsenious  oxide  i3'8o  570° 

„                                       1378  1400° 

From  these  numbers,  and  from  those  of  the  previous  table, 
it  is  apparent  that  the  specific  gravities  of  certain  gases — 
elementary  and  compound  alike — decrease  as  the  tempera- 
ture increases,  while  in  the  case  of  other  gases  the  density 
is  practically  independent  of  the  temperature;  a  limiting  value 
is  however  generally  found  for  the  specific  gravity  of  a  gas. 

It  would  therefore  appear  that  a  chemical  substance  may 
have  more  than  one  molecular  weight ;  but  if  the  mole- 
cule is  the  smallest  part  of  a  substance  which  exhibits  the 
characteristic  properties  of  that  substance,  this  is  equivalent 
to  saying  that  certain  substances  when  heated  may  pass 
through  a  succession  of  changes,  each  phase  being  marked  by 
the  existence  of  a  distinct  kind  of  matter.  More  accurate 
experiment  has  shewn  that  the  vapours  of  phosphorus  pen- 
tachloride  and  nitrogen  tetroxide,  at  high  temperatures,  are 
mixtures  of  phosphorus  trichloride  and  chlorine,  and  of 
nitrogen  tetroxide  and  nitrogen  dioxide  (N2O4  and  NO2) 
respectively,  so  that  at  these  temperatures  we  have  to  deal 
not  with  homogeneous  vapours,  but  with  mixtures  of 
different  gases,  varying  in  composition  at  different  moments. 
The  connection  existing  between  temperature  and  the  den- 
sities of  gaseous  elements  and  compounds  will  be  examined 
in  more  detail  in  a  future  chapter1  (see  Book  II.). 

The  practical  outcome  of  these  considerations  is  that  in 
determining  a  molecular  weight  the  gas  must  be  proved  to 
be  really  a  homogeneous  substance,  and  not  a  mixture  pro- 

1  Avogadro's  law  may  be  deduced  from  the  molecular  theory  of  matter,  but 
inasmuch  as  this  theory  is  based  upon  more  or  less  inexact  hypotheses,  and  is  as 
yet  but  in  an  early  stage  of  development,  inasmuch  also  as  the  deductions  made 
from  it  concerning  gaseous  laws  are  strictly  applicable  only  to  'perfect  gases,'  it 
follows  that  Avogadro's  law  cannot  be  regarded,  at  present,  as  absolutely  true. 
The  laws  of  Boyle  and  of  Charles,  which  are  also  deducible  from  the  molecular 
theory,  do  not  give  a  complete  account  of  the  relations  of  gases  to  temperature  and 
pressure. 

M.  C.  3 


34  CHEMICAL   STATICS.  [§  I/ 

duced  by  the  decomposing  action  of  heat  on  the  original  sub- 
stance ;  and,  further,  that  the  value  obtained  for  the  specific 
gravity  must  be  constant  throughout  a  considerable  range  of 
temperature. 

17.  In  determining  the  density  of  a  gas,  especially  if  at 
a  somewhat  high  temperature,  many  sources  of  error  are 
present ;  the  result  cannot  therefore  be  more  than  mode- 
rately accurate1.  But  experimental  errors  are  more  easily 
avoided  in  the  determination  of  the  combining  weight  of  an 
element,  that  is,  the  quantity  of  the  element  found  in  combi- 
nation with  one  part  by  weight  of  hydrogen,  7*98  parts  by 
weight  of  oxygen,  or  35*37  parts  by  weight  of  chlorine.  Now 
it  is  evident  that  the  molecular  weight  of  an  element  must 
be  equal  to,  or  a  multiple  of  its  combining  weight,  and  the 
molecular  weight  of  a  compound  must  be  equal  to  the  sum, 
or  to  a  multiple  of  the  sum  of  the  combining  weights  of  its 
constituent  elements.  Hence  if  the  combining  weight,  and 
the  specific  gravity  in  the  gaseous  state  of  an  element  are 
carefully  determined,  we  have  the  necessary  data  for  an 
accurate  determination  of  the  molecular  weight  of  that  element; 
the  combining  weight  being  an  accurately  determined  num- 
ber, and  the  specific  gravity  deciding  what  multiple  of  that 
number  represents  the  molecular  weight.  So  also  the  data 
required  for  an  accurate  determination  of  the  molecular 
weight  of  a  compound  are,  the  combining  weights  of  the 
constituent  elements,  and  the  specific  gravity  of  the  com- 

1  Dumas'  method  for  determining  vapour  densities  is  described  in  Ann.  Chim. 
Phys.  [2]  33.  337  •  Gay  Lussac's  in  Biot's  Traite  de  Phys.  1.  291;  Hofmann's 
in  Ber.  1.  198;  and  Victor  Meyer's  Ber.  11.  1868  and  2253.  For  criticisms  on, 
and  modifications  of  Meyer's  method  see  Ber.  12.  609  and  1112:  13.  401,  851, 991, 
1079,  Il85>  and  20J9  '  14.  1727:  and  15.  137,  1161  and  2775:  (in  the  last  paper  by 
V.  Meyer  [Ber.  15.  2775]  will  be  found  an  interesting  and  valuable  criticism  of 
the  various  methods  for  finding  the  Sp.  Grs.  of  gases).  See  also  Ber.  16.  1051; 
also  C.  S.  Journal  Trans,  for  1880.  491.  Modifications  of  Dumas'  method 
are  described  by  Bunsen,  see  Gasometrische  Methoden,  2nd  ed.  (1877),  p.  172: 
also  by  Petterson  and  Ekstrand,  Ber.  13.  1191:  and  especially  by  Pawlewski, 
Ber.  16.  1293.  Thorpe  [C.  S.  Journal  Trans,  for  1880.  147 — 150]  has  de- 
scribed a  very  complete  method  based  on  Hofmann's  process.  V.  Meyer  [Ber. 
9.  1260:  and  10.  2068]  has  described  a  method  based  on  the  displacement  of 
mercury. 


§  1  8]  ATOMS   AND   MOLECULES.  35 

pound  in  the  state  of  gas.  Thus  Regnault  found  for  the 
specific  gravity  of  chlorine  the  number  2^44,  which  multiplied 
into  28*87  gives  70*44.  The  combining  weight  of  chlorine  as 
most  carefully  determined  by  Stas  is  35*37:  now  35*37x2 
=  7074,  which  is  very  nearly  equal  to  the  molecular  weight 
calculated  from  Regnault's  numbers,  hence  70*74  is  taken  to 
be  the  molecular  weight  of  chlorine.  Again,  Thomson  found 
the  specific  gravity  of  marsh  gas  to  be  0*557,  which  multiplied 
into  28^87  gives  16*1  as  approximately  the  molecular  weight 
of  this  compound  :  the  combining  weight  of  carbon  is  2*99 
(H  =  i),  and  in  marsh  gas  carbon  and  hydrogen  are  united  in 
the  proportion  of  2*99  to  I,  hence  the  molecular  weight  of  this 
gas  is  3*99  or  a  multiple  thereof.  But  3*99  x  4=  15*96,  there- 
fore the  molecular  weight  of  marsh  gas  is  taken  to  be  15*96. 

The  numbers  in  column  V  of  the  table  on  p.  31  represent 
the  molecular  weights  of  the  various  elements  found  by  the 
method  of  specific  gravity  aided  by  determinations  of  the 
combining  weights  of  the  elements  in  question. 

1  8.  Facts  have  already  been  mentioned  which  on  the 
assumption  of  the  truth  of  Avogadro's  law  oblige  us  to 
conclude  that  in  certain  chemical  reactions  the  molecules  of 
the  reacting  elementary  bodies  undergo  subdivision  ;  indeed 
we  are  forced  to  the  conclusion  that  the  greater  number  of 
the  elementary  molecules  are  not  homogeneous  but  are  built 
up  of  smaller  parts1.  Now  it  is  evident  that  the  molecule 
of  an  element  cannot  contain  less  than  two  of  these  smaller 
parts  or  atoms,  unless  indeed  the  atom  and  molecule  should 
be  identical  ;  and  that  the  molecule  of  a  compound  cannot 
contain  less  than  one  atom  of  each  of  its  constituent  elements. 
Therefore  if  we  determine  the  smallest  amount  by  weight 
of  an  element  in  the  molecule  of  any  compound  thereof,  we 
shall  have  determined  the  maximum  atomic  weight  of  the 
element  in  question. 

Hence  we  arrive  at  the  following  definition. 

1  Reactions  are  known  in  which  it  is  not  necessary  to  assume  that  subdivision 
of  elementary  molecules  occurs,  e.g. 


Volumes     4+  4  =4. 

3—2 


CHEMICAL  STATICS. 


[§I9 


The  maximum  atomic  weight  of  an  element  is  the  smallest 
quantity,  in  terms  of  hydrogen  as  unity,  of  that  element  in  the 
molecule  of  any  compound  thereof. 

Molecular  weight  has  been  already  defined  as  weight  of 
two  volumes  of  any  gas  referred  to  the  weight  of  two  volumes 
of  hydrogen ;  hence  the  data  which  must  be  obtained  before 
the  maximum  atomic  weight  of  an  element  can  be  determined 
are,  (i)  specific  gravity  of  a  series  of  gaseous  compounds  of 
the  element  in  question,  and  (2)  careful  analyses  of  these 
compounds.  Suppose  it  is  required  to  determine  the  maxi- 
mum atomic  weight  of  oxygen,  such  data  as  are  indicated  in 
the  following  table  are  obtained. 

Data  for  determining  maximum  atomic  'weight  of  oxygen. 


Name  of  compound 

Weight  of  2  volumes, 
as  gas,  referred 
to  hydrogen 

Analysis  of  these  2  volumes 

Water 

I7-99 

15-96  oxygen  +  2  hydrogen 

Carbonous  oxide 

27-96 

J5'96       3J      +11*97  carbon 

Carbonic  dioxide 

44-I5 

31-92       „      +11-97       „ 

Nitrous  oxide 

43*9 

15-96       „      +28*02  nitrogen 

Methylic  alcohol 

32-3 

(15-96       „      +ii"97      carbon 
\                        +  4  hydrogen 

Methyl  nitrate 

76-2 

(47-88       „       +11-97  carbon 
\  +3  hydrogen  +14-0  1  nitrogen 

Nitric  oxide 

50-0 

15-96  oxygen+  14-01  nitrogen 

Sulphurous  oxide 

64-9 

31-92       „       +  3i'98  sulphur 

Sulphuric  oxide 

86-9 

47-88       „      +31-98       „ 

Phosphorus  oxychloride 

I55'9 

J5'96       j?     +30-96  phosphorus 

+  1  06'  1  1  chlorine 

Osmium  tetroxide 

257 

63*84       „      +198*6  osmium 

If  the  smallest  weight  of  hydrogen  found  in  a  molecule 
of  any  compound  of  that  element  is  called  one,  then  in  no 
molecule  of  any  of  the  compounds  in  this  table  is  there  less 
than  15*96  parts  by  weight  of  oxygen  ;  this  number  is  there- 
fore adopted  as  the  maximum  atomic  weight  of  oxygen. 

19.  The  following  table  (taken  for  the  most  part  from 
Lothar  Meyer's  Die  modernen  Theorien  der  Chemie)  contains 
the  most  important  data  hitherto  accumulated  for  determining 
the  maximum  atomic  weights  of  the  elements  by  the  applica- 
tion of  Avogadro's  law. 


19] 


ATOMS   AND   MOLECULES. 


37 


c   2  <u 

|l  ** 

S  ^ 

W5    Jj  ^ 

1°  3 

>  K  '3 


4»    C  yr; 

'!  1 

r-     O  <« 

S       ^  <+H 

il  i 


c 

Is 


=-««         -°     . 

IOS-B? 

S.2  .|  I 


§•§ 


<u  "^  rt 


Si 

'o  -a 


IPl?l-8 


HSS  1| 

^.s  §1 

l|f|i 

«    X         ^3 


>  5S 


vo  coovort- 

,  ON  ON  ONOO  \OCOONtoQONON  *-1 


O  MD    O    Kx  t^  fO  rO  ON  ^f  O    O    ON  t^  ON 

n  moo  N  --I  co>o  r^  cooo  «<N'-IM 


O  MD  00  CO   K  ^-  -^t-MD      j-  OO    ON        O    «O 
C^    CO  T^  M    •->    CO\O  CO    COCO    M    M    HH    CO  ^ 


$2 


>-" 


«-  rt-     M  HH 


..  « 


.     o  -Q) 

C" 

5    a  'S 


S  g. 

5   o< 


fill 


ll 


38 


CHEMICAL  STATICS. 


[§I9 


gig 

III 


§  2  + 

^cls 

>>r-(       O 


»_       •- 

03    rt 
(J    U 


+ 

2      S 

:  <u-5 

ill 

H      ON    "H 
H      10    1-1 

;  grfcis 

,      CO    HH      HH 


+  R 

+ 
d 

;|s 
gg5 

vO  "^ 
.^^ 
to^-1 
CO 


I 


i-n 


u^ 

6C 


| 

T3 
£  >-, 


"  +  3 

£i£  +    £  +  « 

]!I|IPU 
1=3-1  H!3!| 

t^HlOOtOHH      N      HH^'^ 

co  p  op  ^x  oo  vx  r° 


p  .< 
^•Qb<DQbbo^*p^^"*"t 

HI   cococococococo" 


O  O 


a 


OOtNlOHHtX^HHCO          O 


IN  O 


to  covO  IN.O   coONCorNHH    O    O   ON 
vO   ^O  C^    co  HH   tovO   co  t^sOO   ^t"  covO   ] 

HH      HH      ^-    HH      HH      HH  HH      HH      HH      HH 


O   to  to  ^  O   '^J'1-1 


vO  •-"  M  ON  HH  ON  INOO  OO  ON  IN  IN.  ^-00  tNOO  INOO  OO  O  yo  IN  O  co  I-H  ON  O  fO 

VO     COCOO    rNty-iQNM    tN  HH     HH     COCO'^t''xi""^t'  INVO     COVO     CO  tOVO     '"^  'O     CO  HH     HH 
VO    CO^O    ^  "-1    >-O^O    CO  tNCO    CO  CO  INVD     n    HH    MVO    >-<    "H    tOtr^HH    COlOON'^-n 


i-i  io  ONOO  vO  O  oo 

p    HH       HH    00       f*   I*  "  " 

M    HH    N    rj-  Tj-  io  to  ^f-  N  vO 


3$ 


M  00 

tN  tN   HH     h 


M    M  lOMD  vO   co  fO 

10  I-H    Tj-  M  OO    <O  LOOO    CO  lOOO    O 
coco^O 


-H    O    i-i    1-1   co  ^  ^- 


19] 


ATOMS   AND   MOLECULES.  39 


fl      sJlafL  S&  gl    .  .     g          a 

r2  £<       o  S   *   °   O  bJ°°  bfl  ^     ~    ~        bJO  <u 

'y^r^UOOp^  ^'d  J-,^  M 

4-  ^          -L^  JL  •!•         4- 

,     s|s|j§|  •••jlslljlil 

•gfiiai-el      •l||||i||| 


o       N  P  r^  HH 

1-!    O 

!-|  _,      CO    l-l      "-HVO      HH      HH      "H      «      "1      1^    "H      lf\    &    •-<'    ~      <->      - 


ON  r^  >-i    roco 
^h      ON  00  ^D    ON  ON  ON  CO  ON  pNOO    ^t  i-T>  HH  OO    — 

' 


to     t^  cooc    ON  u~vMD    <->    N    i—  <      '^|-ONI-COI-'NONI-I    ONMD  oo   co  O      h  ON  ONMD   t^  LO     "  N    ^ 

ro  vr>  coco   to  ^J-oo  oo   covO  r^  co  ON  H  r^ 


co  ON  ON  M    p  OO   ^-  rf-  yr>  fO  co  N    O   ^  ^t  J->    ON  u^  rf  j^  p    N  vp    ^t  rh  _M    rf  N   f  J  CO    O    O    O 


M    COM^O    CO  M    MOO    rOt>">  LOCO  VO    "H    CO^O  CO 


M    i-i  \p  00    I-H    C^    pN^J-p    Tj-  ON  fO  CS  VO    y 
O    «    fO  O    N    «    «    N    CO    ^  ON  LT>  ^-\b  00    ON  K-O  COCJO    ONOCO 


0)    O 

:g!2,« 

-§        ojj  ^  ,%  II?     . 

T3 


2  -x^^^^  ^  s    ^  o^sS?  §^  s^^'S  ^^^^-^6^         a 

cj      o^-d^Q-       I-H        'S  Js  TS  »S  T3  J  ^?  «S  «r3  *C   S   O  JS   H   ?«  _fl   B  «  12    ..    .  o 


CHEMICAL  STATICS. 


[§I9 


t^   !>..    HH     LO   CO   ON   O  HH 

ON  t^x  *-o  O    ON  C^    t\  *-O  C^N,  C^ 

N   i_n  ro  r^  u->  ur,  ui  \f\  HH  r^ 

C^C^NC^co^M  HH  NM 


'-i-\o  ci  co  i^  b 
co  n  >-ooo  HH  co 


rJ-00  Vp    O    O    O    O    O    O    W    O    O    O    O    O    O    O    O    O    ONOO 

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3     nX£     U     U    ^H     XS-5     G     2     ^ 
«_     ^H     C     X     *>~\  TT     ^     r^     K^      r?     J-i     J-H 


jg 
o 

1 1 1 1|  JTJ  s  s 


rin         , 

U         H^ 


3%v 

C  c  ^  o 
<u|o^3  o 

:s-g£.2  S^ 

^  S  S  S^.2 

^333 

U'S'S 
•cfi'§B^ 

^    3  3  5    3  ^ 

«uo 


n 
ous 
c  c 


Fe 
Al 


ml  ATOMS  AND  MOLECULES. 

\fi*S.' 
^&>*, 

.v:t 


/<?  //z<?  preceding  Table. 


1  The  density  of  hydrofluoric  acid  was  determined  indirectly  by  Gore  (P 
Trans,  for  1869.  173)  at  100°.     Mallet  (Amer.  Chem.  Journal  3.  189)  by  directly 
weighing  i  litre  of  the  gas  at    30°  found  the  specific  gravity  to  be  1*42,  which 
gives  a  molecular  weight  of  4  ['02.     The  molecular  weight  of  this  gas  therefore 
decreases  as  temperature  increases. 

2  and  3  Indirectly  determined  by  Bineau  (Ann.   Chim.  Phys.  [2]  68.  424);  two 
volumes  of  each  hydride  when  decomposed  by  metal  yielded  2  vols.  of  hydrogen, 
78  parts  by  weight  of  selenion  in  one  case,  and  128  parts  by  weight  of  tellurium 
in  the  other  being  produced. 

4  At  a  temperature  slightly  above  its  boiling  point  the  specific  gravity  of 
gaseous  stannous  chloride  points  to  the  molecular  weight  377;  but  at  200°  higher 
the  specific  gravity  is  as  given  in  the  table  ;  this  gas  therefore,  like  hydrofluoric 
acid,  has  two  molecular  weights:  see  Meyer  and  Ziiblin  (fier.  13.  811). 

6  There  is  some  doubt  whether  the  vapour  of  mercurous  chloride  does  or 
does  not  contain  mercury  and  mercuric  chloride  :  the  number  in  the  table  is  from 
a  paper  by  Fileti,  who  states  that  by  vaporising  a  mixture  of  the  two  chlorides 
of  mercury,  the  protochloride  remains  undissociated  (see  abstract  of  Fileti's  paper 
in  C.  S.  Journal  Abstracts  for  1882.  466). 

6  Chromium   hexfluoride  (CrF6)  is   frequently  mentioned  in  text-books  as  a 
gaseous  compound  of  chromium  ;  the  evidence  in  favour  of  the  existence  of  a 
definite  fluoride  of  chromium  is  meagre,  no  determinations  of  its  density  (if  it 
exists)  have  been  made;  see  Unverdorben  (Pogg.  Ann.  7.  311). 

7  Odling  \_Phil.  Mag.  [4]  29.   316)  gave   the   specific   gravity  of  aluminium 
tetramethide  at  temperatures  above  200°  as  2*5,  and  at  130°  as   5*0;  but  it  is 
undecided  whether  the  gas  at  200°  was  homogeneous  or  a  mixture  of  the  products 
of  decomposition  by  heat  of  molecules  existing  at  lower  temperatures  (see  Wanklyn 
loc.  cit.  313  and  Williamson  do.  395).     If  the  gas  at  200°  was  really  homogeneous, 
we  should  have  2*5  x  28*87  =  72*5  as  the  molecular  weight  of  aluminium  tetra- 
methide, and  this  quantity  of  the  gas  contains  27*3  aluminium  +35*91  carbon 
+  9  hydrogen  (=72-21). 

8  At  450°  the  sp.  gr.  of  the  vapour  of  gallic  chloride  is  7*8,  and  at  the  same 
temperature  in  presence  of  an  indifferent  gas  acting  as  diluent,  it  is  6*6:  the  gas 
dissociates  under  these  conditions.     (See  Lecoq  de  Boisbaudran,  Compt.  rend.  93. 
294,  329  and  815.) 

The  maximum  atomic  weights  deduced  from  these  data 
may  in  many  cases  be  regarded  with  a  large  degree  of  proba- 
bility as  the  true  atomic  weights  of  the  elements.  The 
greater  the  number  of  gaseous  compounds  of  an  element 
analysed,  the  greater  is  the  probability  that  the  number  which 
represents  the  smallest  amount  of  that  element  in  two  vol- 
umes of  any  of  these  compounds  is  the  true  atomic  weight 
of  the  element. 


CHEMICAL   STATICS. 


2O 


20.  When  the  atomic  and  molecular  weights  of  an  ele- 
ment are  known,  the  atomicity  of  the  molecule,  i.e.  the  number 
of  atoms  in  the  molecule,  is  known. 

In  the  following  table  the  molecules  of  the  elements,  so 
far  as  the  relative  weights  of  these  have  been  determined  by 
the  method  founded  on  Avogadro's  law,  are  classified  in 
accordance  with  their  atomicity. 

Atomicity  of  Elementary  Molecules^. 


Monatomic 

Diatomic 

Triatomic 

Tetratomic 

Hexatomic 

Cadmium 

Hydrogen 

Oxygen  (ozone) 

Phosphorus 

Sulphur 

Mercury 

Chlorine 

Selenion 

Arsenic 

(450°  to 

Iodine 

Bromine 

(700°  to  800°) 

about  550°) 

(at  about  1  500°) 

Iodine 

(?  Bromine  at 

(200°  to  about 

about  1800°) 

1000°) 

Oxygen 

Sulphur 

(at   800°   and 

upwards) 

Selenion 

(at  1200°  and 

upwards) 

Tellurium 

Nitrogen 

The  molecules  of  the  majority  of  the  elements  in  this 
table  are  diatomic,  but  inasmuch  as  the  molecular  and  atomic 
weights  of  only  13  elements  have  been  determined  it  is  im- 
possible to  say  whether  a  majority  of  all  the  elementary 
molecules  contain  each  two  atoms.  It  ought  also  to  be 
observed  that  of  the  13  elements  in  the  table,  five  have  more 
than  one  molecular  weight,  and  therefore  exhibit  the  phe- 
nomenon of  varying  atomicity. 

The  table  contains  two  well-defined  metals,  cadmium  and 
mercury ;  the  molecules  of  these  elements  are  monatomic, 
and  hence  are  of  a  simpler  structure  than  the  molecules  of 
those  elements  which  possess  in  a  marked  manner  the  pro- 
perties summed  up  in  the  term  nonmetal. 

1  This  table  shews  that  many  elementary  gases  have  complex  structures; 
hence  arise  difficulties  in  forming  accurate  physical  conceptions  of  actions  and 
reactions  among  the  parts  of  these  structures.  This  will  be  again  referred  to  when 
dealing  with  atomic  heats  (see  pp.  64 — 5). 


§2l]  ATOMS   AND   MOLECULES.  43 

21.  Chemical  formulae  for  the  most  part  profess  to  repre- 
sent not  only  the  elementary  composition,  but  also  the  rela- 
tive weights  of  the  molecules,  of  the  bodies  formulated  :  but 
unless  some  method  for  determining  molecular  weights  other 
than  that  founded  on  Avogadro's  law  is  adopted,  it  is  evident 
from  the  data  in  the  table  on  pp.  37 — 40  that  the  majority  of 
the  formulae  employed  in  mineral  chemistry  cannot  be  said 
to  be  certainly  molecular  formulae.  Thus  analysis  shews  that 
17-96  parts  by  weight  of  water  contain  15*96  parts  of  oxygen 
and  2  parts  of  hydrogen  ;  analysis  also  shews  that  5837  parts 
by  weight  of  sodium  chloride  contain  23  parts  of  sodium  and 
35-37  parts  of  chlorine.  The  specific  gravity  of  water  vapour 
shews  that  the  molecular  weight  of  this  compound  is  about 
1 8,  hence — assuming  the  atomic  weight  of  oxygen  to  be 
15-96 — the  molecular  formula  is  written  H2O  (i7'96).  But  no 
determination  of  the  density  of  sodium  chloride  vapour  has 
yet  been  made  ;  hence  the  molecular  weight  may  be  about  59', 
or  it  may  be  a  multiple  of  this  number  (assuming  the  atomic 
weights  of  sodium  and  chlorine  to  be  known),  and  hence  the 
formula  NaCl  (58-37)  is  not  necessarily  molecular,  and  is 
therefore  not  strictly  comparable  with  the  formula  H2O. 

Even  if  a  formula  does  express  the  relative  weight  of  the 
molecule  of  the  body  formulated  it  is  well  to  remember  that 
it  is  the  weight  of  the  gaseous  molecule  which  is  thus  ex- 
pressed ;  the  formula  does  not  necessarily  also  represent  the 
relative  weight  of  the  molecule  of  the  same  body  when 
solid. 

As  a  general  rule,  the  melting  and  boiling  points  of  sub- 
stances with  large  molecular  weights  are  high ;  thus  in  any 
homologous  series  of  hydrocarbons  the  boiling  and  melting 
points  increase  with  increase  of  molecular  weight1 ;  the  same 
connection  between  these  constants  is  noticed  in  many  series 
of  oxides,  e.g.  the  oxides  of  nitrogen2.  It  would  therefore 
appear  probable  that  the  molecular  weight  of  a  solid  is  greater 

1  Thus,        C4H10,  C5H12,  C6H14,  C7H16,  C8H18,  C9H20,  C10H22  £c. 
B.  P.  =          i°         38°         70°         99°        124°       148°       167°    &c. 

2  NO  N2O  N2O3         N2O4         N2O5 
gaseous  at  -  rio°,  B.  P.  =  -88°,  about  -20°,     22°,     M.  P.  =30°. 


44  CHEMICAL   STATICS.  [§22 

than  that  of  the  same  substance  when  in  the  state  of  gas.  So 
also,  as  a  rule,  the  action  of  heat  produces  molecules  of  less, 
from  those  of  greater  weight.  Thus  N2O4  which  exists  at 
low  temperatures  becomes  NO2  when  heated  (see  numbers 
on  p.  32)  ;  so  S6  exists  at  500°,  but  S2  at  1000° :  at  tem- 
peratures above  300°  the  molecule  O3  decomposes  into  O2. 
Reactions  are  known  in  which  heat  appears  to  favour  the 
production  of  molecules  of  greater  weight  and  complexity 
than  those  previously  existing  ;  but  these  more  complex  mole- 
cules only  mark  intermediate  stages  towards  the  formation 
of  less  complex  and  comparatively  lighter  molecules.  Thus 
the  action  of  heat  on  sodium-hydrogen  sulphate  is  generally 
formulated  in  two  stages,  (i)  2NaHSO4  =  Na2S2O7  +  H2O  :  (2) 
Na2S2O7  =  Na2SO4  +  SO3.  So  also  when  mercuric  cyanide  is 
decomposed  by  heat  molecules  of  cyanogen  are  produced, 
having  the  formula  (CN)#  where  u>  2,  but  at  800° — 900° 
these  are  dissociated  into  the  lighter  molecules  C2N2.  Lead 
monoxide  (PbO);/  when  heated  forms  the  heavier  oxide 
(Pb3O4);/,  &c.:  in  many  of  these  cases  however  we  are  not 
certain  that  the  formulae  employed  represent  the  relative 
weights  of  molecules. 

The  physical  phenomena  presented  by  liquids  and  solids 
cannot  be  expressed  by  such  comparatively  simple  generali- 
sations as  those  which  express  the  properties  of  gases;  the 
molecular  phenomena  of  the  former  classes  of  bodies  are 
evidently  more  complex  than  those  of  the  latter  class.  Great 
caution  must  therefore  be  used  in  applying  deductions  made 
from  the  study  of  the  molecular  phenomena  of  gases  to 
solid  or  liquid  bodies1. 

22.  The  following  table  gathers  together  the  results  of 
the  observations  recorded  in  the  table  on  pp.  37 — 40,  so  far  as 
regards  the  maximum  atomic  weights  of  elements  determined 
by  the  application  of  Avogadro's  law  : 

1  The  comparison  of  the  molecular  phenomena  of  gases  with  those  of  solids 
and  liquids  will  be  considered  more  fully  in  a  future  chapter. 


§  23]  ATOMS   AND   MOLECULES.  45 

Maximum  atomic  weights  of  elements.     (AvOGADRO's  law.) 


Name 

Maximum 
atomic 
weight 

Name 

Maximum 
atomic 
weight 

Name 

Maximum 
atomic 
weight 

Hydrogen 

I 

[Aluminium 

54-04J1 

Iodine 

126-53 

Boron 

IQ'95 

Zinc 

64-9 

[Copper 

I  26-8]  ! 

Carbon 

II'97 

Arsenic 

74-9 

Tellurium 

I27-5 

Nitrogen 

I4-OI 

Selenion 

78-8 

[Gallium 

138? 

Oxygen 

15-96 

Bromine 

7975 

Tantalum 

182 

Fluorine 

19'! 

Zirconium 

90 

Tungsten 

183-6 

Silicon 

28 

Niobium 

94 

Osmium 

195  (?) 

Phosphorus 

30-96 

Molybdenum 

95-8 

Mercury 

I99-8 

Sulphur 

31-98 

[Iron 

in-8]1 

Thallium 

203-64 

Chlorine 

35'37 

Cadmium 

112 

Lead 

206'4 

Titanium 

48 

Indium 

113*4 

Bismuth 

208 

Vanadium 

51*2 

Tin 

II7-8 

Uranium 

240 

Chromium 

52-4 

Antimony 

120 

About  half  of  the  known  elements  are  found  in  this  table. 

Some  method  other  than  that  based  on  the  determination 
of  the  specific  gravities  of  gaseous  compounds  must  if  possible 
be  discovered  for  finding  the  atomic  weights  of  the  elements. 

23.  In  his  New  System  of  Chemical  Philosophy*  (pp.  70 — 
75),  Dalton  discusses  hypotheses  regarding  the  quantities 
of  heat  contained  in  various  elastic  fluids,  and  decides 
in  favour  of  that  which  asserts  'the  quantity  of  heat  be- 
'  longing  to  the  ultimate  particles  of  all  elastic  fluids  must 
'be  the  same  under  the  same  pressure  and  temperature.' 
From  this  Dalton  deduced  the  corollary  '  the  specific  heats  of 
'  equal  weights  of  any  two  elastic  fluids  are  inversely  as  the 
'weights  of  their  atoms  or  molecules.'  The  values  of  very 
few  specific  heats  had  been  determined  when  Dalton  wrote, 
and  therefore  he  did  not  possess  data  sufficient  to  test  the 
justness  of  his  general  principle.  Dalton  calculated  the 
theoretical  specific  heats  of  various  gases  by  the  aid  of  the 
above  corollary,  employing  atomic  weights  determined  by 
himself.  Regarding  the  table  of  numbers  thus  obtained  he 
remarks  '  upon  the  whole  there  is  not  any  established  fact  in 

1  Especial  reference  will  be  made  to  those  elements  in  brackets  in  a  later 
paragraph  :  see  p.  56. 

2  Published  in  1808. 


46  CHEMICAL   STATICS.  [§  24 

'  regard  to  the  specific  heat  of  bodies,  whether  elastic  or  fluid, 
'  that  is  repugnant  to  the  above  table  so  far  as  I  know;  and  it 
'  is  to  be  hoped  that  some  principle  analogous  to  the  one  here 
'  adopted  may  soon  be  extended  to  solid  and  liquid  bodies  in 
'  general.' 

In  1819  a  paper  by  Petit  and  Dulong  appeared  in  the 
Annales  de  Chimie  et  Physique  [10.  395],  containing  the  results 
of  determinations  of  the  specific  heats  of  thirteen  solid  ele- 
ments, viz.  copper,  gold,  iron,  lead,  nickel,  platinum,  sulphur, 
tin,  zinc,  bismuth,  cobalt,  silver,  and  tellurium.  A  nearly 
constant  product  was  obtained  by  multiplying  the  specific 
heats  of  the  nine  elements  from  copper  to  zinc,  in  this  list, 
by  the  then  generally  accepted  atomic  weights  of  these 
elements,  and  the  specific  heat  of  bismuth,  cobalt,  silver, 
and  tellurium  by  a  sub-multiple  of  the  accepted  atomic  weight 
of  each  of  these  elements.  Generalising  from  these  results 
the  French  physicists  concluded  that  'the  atoms  of  all  the 
'  simple  bodies  have  exactly  the  same  capacity  for  heat.' 

The  introduction  of  more  accurate  methods  for  determin- 
ing specific  heats  has  necessitated  considerable  alterations  in 
many  of  the  numbers  to  be  found  in  the  original  paper  of 
Petit  and  Dulong,  nevertheless  their  general  conclusion  re- 
mains, although  it  cannot  now  be  stated  in  terms  quite  so 
absolute  as  those  used  by  its  promulgators. 

24.  In  1831  F.  Neumann1  published  determinations  of 
the  specific  heats  of  various  solid  compounds,  chiefly  of 
naturally  occurring  minerals,  and  deduced  the  general  state- 
ment, '  The  amounts  of  chemically  similar  compounds  ex- 
'  pressed  by  their  formulae  possess  equal  specific  heats.' 

A  few  years  later  (1833 — 4)  Avogadro2  detailed  measure- 
ments of  the  specific  heat  of  carbon,  and  of  various  com- 
pound substances,  and  drew  certain  general  conclusions  there- 
from; he  spoke  of  those  atomic  weights  which  were  deduced 
from  measurements  of  specific  heats  as  the  weights  of  thermal 
atoms  (atonies  thermiqiies). 

1  Fogg.  Ann.  23.  i.     Neumann  measured  the  specific  heats  of  8  carbonates, 
4  sulphates,  4  sulphides,  5  oxides  of  the  type  MO,  and  3  of  the  type  M2O3. 

2  Published  in  condensed  form  in  Ann.  Chim.  Phys.  [2]  55.  80:  and  57.  113. 


§  24]  ATOMS   AND   MOLECULES.  47 

R.  Hermann1  made  a  number  of  determinations  of  specific 
heats,  and  from  these  deduced  the  combining  weights  of 
several  elements.  The  weights  thus  obtained  were  in  some 
cases  different  from  the  Berzelian  weights  then  in  general  use. 
Hermann  supposed  that  the  specific  heat  of  certain  elements, 
e.g.  sulphur  and  oxygen,  varies  according  as  the  element  is 
in  the  free  state  or  in  combination  with  other  elements. 

Regnault2,  in  a  series  of  classical  memoirs  added  much  to 
our  knowledge  of  specific  heats,  and  gave  a  general  confirma- 
tion to  the  laws  of  Dulong  and  Petit,  and  of  Neumann.  He 
arranged  a  table  of  so-called  thermo-atomic  weights :  (see 
table). 

Regnaiilfs  Thermo-atomic  weights.     [See  KOPP,  loc.  tit.] 

Al  =137  Cr  =26-1  Mn  =  27'5  86=397 

Sb  =61  Co  =29-4  Hg=ioo  Ag  =54 

As  =37-5  Cu=3i7  Mo  =  48  Na  =  ii'5 

Ba=68'5  F    =9-5  Ni  =29-4  Sr=43'8 

Bi  =105  Au=98'5  N    =7  S     =16 

B    =10-9  I     =63-5  Os  =99-6  Te  =64 

Br  =40  Ir    =99  Pd  =53-3  Tl   =102 

Cd=s6  Fe  =28  P    =15-5  Sn  =59 

Ca  =20  Li  =3-5  Pt  =987  Ti  =25 

C    =12  Pb=  103-5  K    =19-5  W  =92 

Cl  =1775  Mg=i2  Rh  =  52'2  Zn  =32-6 

Gamier3  (in  1852)  further  generalised  the  relations  between 
formula  and  specific  heat  of  solid  compounds  ;  and  Canniz- 
zaro4  advanced  somewhat  the  generalisation  of  Gamier. 

The   Garnier-Cannizzaro    generalisation    may   be    stated 

A  C 

thus  :  — '- —  =  constant  (about  6*4),  where  A  =  formula-weight 

of  a   compound,  C  =  specific  heat  of  same  compound,  and 
n  =  number  of  elementary  atoms  in  the  formula. 

1  Nouveaux  Memoires  de  laSociete  Imperials  des  Natttralistes  de  Moscou  (1834). 
3.  137. 

2  Ann.  Chim.  Phys.  [2]  63.  5.  [3]  1.   129:  9.  322:  26.  261  and  268:  38.  129: 
46.  257:  63.  5. 

3  Compt.  rend.  35.  278:  37.  130. 

4  //  Nuovo  Cimento  1.  321;  Abstract  in  Bull.  Soc.  Chim.  for  1863.  171. 


48 


CHEMICAL  STATICS. 


[§25 


25.  Kopp1  has  gathered  together  most  of  the  trustworthy 
results  of  specific  heat  determinations,  and  added  many  of 
his  own,  besides  discussing  the  whole  subject  in  detail. 

.  Table  of  Specific  Heats  of  the  Elements*. 


Name 

Spec, 
heat 

Temp, 

Atomic 
weight 

Sp.  ht. 
X  at.  wt. 

Observer 

Lithium 

0-941 

7-01 

6-6 

Rg. 

1  Beryllium 

0-58 

250° 

9-08 

5'1 

2  Boron 

?o*5 

about  iooo°? 

I0'9 

5  '5 

Wb. 

3  Carbon 

0-463 

980° 

11-97 

5*5 

Wb. 

Sodium 

0-293 

-34°  to  +7° 

23 

6-7 

Rg 

Magnesium 

0-245 

24 

5*9 

Kp. 

^ 

0-25 

5) 

6-0 

Rg. 

Aluminium 

0-202 

27-02 

5*5 

Kp. 

5) 

0-214 

,, 

5-8 

Rg. 

Jj 

0-225 

? 

6-1 

Mt. 

4  Silicon 

0-203 

232° 

28 

57 

Wb. 

Phosphorus  (cryst.) 

0-174 

-  78°  to  +  10° 

30^6 

5  '4 

Rg. 

„ 

0-I89 

„ 

5  '9 

Rg. 

n 

0'202 

6-2 

Kp. 

„        (red) 

0*170 

5*3 

Sulphur 

0-188 

3I-98 

6-c- 

D??. 

„        rhombic 

0-163 

„ 

5-2 

Kp. 

j>              j> 

0-I7I 

5*5 

Bn. 

»              » 

0-I78 

j? 

57 

Rg. 

6  Potassium 

0-166 

-78°  to  +  10° 

59  '°4 

6*5 

Rg. 

Calcium 

OT70 

39'9 

6-8 

Bn\ 

6  Chromium 

O'lO 

52-4 

5*? 

Kp. 

7  Manganese 

0*122 

55 

6-7 

Rg. 

Iron 

0'II2 

55'9 

Kp. 

„ 

0'II4 

6-4 

Rg. 

5J 

o-iio 

55 

6-1 

D.P. 

Nickel 

0-108 

58-6 

6-3 

Rg. 

Cobalt 

0*107 

59 

6-3 

Rg. 

Copper 

0-093 

63-4 

6-0 

Kp. 

„ 

0-095 

n 

6-1 

Rg. 

„ 

0*095 

n 

6-1 

D.P. 

Zinc 

0-0932 

64-9 

6-1 

Kp. 

„ 

0-0935 

?J 

6*1 

Bn. 

5) 

0-0955 

„ 

6-2 

Rg. 

M 

0-093 

?j 

6-0 

D.P. 

8  Gallium 

0-079 

12°  tO  23° 

69 

5  '4 

Bt. 

Arsenic  —  amorphous 

0-076$ 

74'9 

57 

B.W. 

„          crystalline 

0-083$ 

* 

6-2 

B.W. 

1  Annalen,  Supplbd.  3.  i  and  289. 

2  When  no  temperature  is  given  the  determinations  were  made  somewhere 
between  the  limits  o°  and  100° :  the  numbers  may  in  these  cases  be  regarded  as  the 
mean  specific  heats  at  40° — 60°. 


ATOMS   AND    MOLECULES. 


49 


Name 

Spec, 
heat 

Temp. 

Atomic 
weight 

Sp.  ht. 
X  at.  wt. 

Observer 

Arsenic  —  crystalline 

0*0814 

74'9 

6-1 

Rg. 

)>                  » 

0-0822 

6*2 

N. 

9  Selenion  —  amorphous 

0*0746 

-27°  to  +8° 

78*8 

5  '9 

Rg. 

„           crystalline 

0*0745 

-18°  to  +7° 

M 

5  '9 

Rg- 

»                  •» 

0*0762 

6*0 

Rg. 

M 

0*086  1 

6*8 

N: 

»                  „ 

0*084$ 

6*7 

B.W. 

Bromine  —  solid 

0*o843 

-  78°  tO  -  20° 

7975 

6*7 

Rg. 

10  Zirconium 

0*0666 

90*0 

6-0 

M.D. 

11  Molybdenum 

0*0722 

95-8 

6-9 

Rg. 

Rhodium 

0*058 

104 

6-0 

Rg. 

Ruthenium 

0*o6  1  1 

104-5 

6*4 

Bn. 

Palladium 

0*059.3 

106*2 

Rg. 

Silver 

0*056 

107*66 

6*0 

Kp. 

„ 

0*0559 

„ 

6*0 

Bn. 

^ 

0-057 

6-1 

Rg- 

Cadmium 

0*0542 

112 

6-0 

Kp. 

5) 

0*0548 

„ 

6*1 

Bn. 

,, 

0*0567 

n 

6*3 

Rg. 

Indium 

0*057 

11  3*4 

6'c 

Bn. 

Tin 

0*0548 

117*8 

6-5 

Kp. 

„ 

0*0559 

„ 

6-6 

Bn. 

„ 

0*0562 

„ 

6-6 

Rg. 

}J 

0*0514 

6-0 

D.P. 

Antimony 

0-0523 

120*0 

6-2 

Kp. 

j, 

0*0495 

M 

5  '9 

Bn. 

„ 

0*0508 

6-0 

Rg. 

5) 

0*0507 

6-0 

D.P. 

Iodine 

0-054I 

126*53 

6-8 

Rg. 

Tellurium 

0-0475 

I27-5 

6-0 

Kp. 

jj 

0-0474 

6-0 

Rg. 

Lanthanum 

0*0449 

I38-5 

6-2 

Hd. 

Cerium 

0*0448 

141 

6*3 

Hd. 

Didymium 

0*0456 

144 

6*5 

Hd. 

Tungsten 

0-0334 

I83-6 

6-0 

Rg. 

Osmium 

0*03  1  I 

193 

6*0 

Rg. 

Iridium 

0*0326 

194 

6*2 

Rg. 

Platinum 

0*0325 

195 

6*4 

Kp. 

J) 

0*0324 

6*3 

Rg. 

„ 

0*0314 

n 

6*3 

D.P. 

12  Gold 

0*0324 

I96*2 

6*0 

Rg. 

13  Mercury  —  solid 

0*0319 

-  78°  to  -  40° 

199-8 

6-4 

Rg. 

14  Thallium 

0*0335 

203*6 

6-8 

Rg. 

Lead 

0*0307 

206*4 

6;3 

Rg. 

„ 

0*0315 

n 

Kp. 

„ 

0*0314 

9 

6*5 

Rg. 

Bismuth 

0*0305 

208 

6-3 

Kp. 

Thorium 

0*0308 
0*0276 

232*4 

6-4 

Rg- 

Nn. 

Uranium 

0*028 

240 

6-6 

Zn. 

1 

M.  C, 


50  CHEMICAL  STATICS.  [§25 

Notes  to  preceding  Talk. 

I  The  number  for  beryllium  is  that  calculated   by  L.  Meyer  from  the  data 
of  Nilson  and  Pettersson  :  for  fuller  discussion  of  specific  heat  of  beryllium  see 
par.  28,  pp.  58,  59. 

2>3>4  Spec,  heats  of  boron,  carbon  and  silicon  are  discussed  on  pp.   59  —  61, 
par.  29. 

5  The  higher  temperature  (+  10°)  is  not  given  in  Regnault's  paper,  but  judging 
from  the  context  it  appears  to  be  approximately  correct. 

6  This  number  for  chromium  is  probably  too  low  ;  see  Kopp,  Annakn>  Supplbd. 
3.  77  (note). 

7  The  specimen  of  manganese  employed  contained  a  little  silicon. 

8  Spec,  heat  of  molten  gallium  between  109°  and  119°  ='0802.     (Berthelot, 
Bull  Soc.  Chim.  31.  229.) 

9  Spec,  heat  of  amorphous  selenion  determined  at  high  temperatures  is  ab- 
normal, because  of  large  quantity  of  heat  absorbed  before  fusion. 

10  Spec,  heat  of  zirconium  calculated  by  Mixter  and  Dana  from  determinations 
made  with  sample  containing  known  quantities  of  aluminium. 

II  The  specimen  of  molybdenum  employed  contained  carbon. 

12  Spec,  heat  of  gold  is  nearly  constant  from  o°  to  600°;  at  900°  sp.ht.  =  'O345; 
and  at  1000°  =  '0352.     [Violle,  Compt.  rend.  89.  702.] 

13  Spec,  heat  of  liquid  mercury  at  55°=  '033  (Regnault). 

14  The  specimen  of  thallium  employed  contained  a  little  oxide. 

The  numbers  marked  with  £  are  probably  too  large  ;  see  Weber's  papers 
referred  to  below. 

The  names  of  the  various  observers  are  abbreviated  in  the  table  : 


/  Ann.  Chim.  Phys.  [2]  73.  5  : 

RG.  stands  for  REGNAULT,  —  his  papers  on  spec,  heat  I  [3]  1.  129  :  9.  322  :  26. 

are  to  be  found  in  J  261  :  38.  129  :  46.  -257  : 
I  63.  5:  and  67.  427. 

KP.  „  ,,  KOPP,  ,,  ,,  ,,  „  Annalen  126.  362:  and 

Supplbd.  3.  i  and  289. 

N.        ,,     ,,    NEUMANN,         ,,        „        „        „        Pogg.  Ann.  126.  123. 

BN.       ,,     ,,     BUNSEN,  „          „         ,,         ,,         Pogg.  Ann.  141.  i. 

WB  .....  WEBER,  „  „  „  „  Pogg.  Ann.  154.  367  [trans- 

lation in  Phil.  Mag.  (4) 
49.  161  and  276.] 

D.  P.    ,,     ,,     DULONG  and  PETIT,     „         „        „       -Ann.  Chim.  Phys.  10.  395. 

BT.       ,,     ,,     BERTHELOT,       „        ,,        ,,        ,,        Compt.  rend.  86.  786. 

HD.  ,,  ,,  HILLEBRAND,  ,,  „  „  ,,  Pogg.  Ann.  163.  71  [trans- 

lation in  Phil.  Mag.  (5) 
3.  109]. 

B.  W.  ,,     ,,     BETTENDORFandWuLLNER  „       „         Pogg.  Ann.  133.  293. 

M.  D.  ,,     ,,     MIXTER  and  DANA,     „        „        „        Annalen,  169.  388. 

NN.      „     ,,     NILSON,  „        „        „        ,,        Ber.  15.  2519. 

MT.      ,,     ,  ,     MALLET,  ,,        ,,        ,,        ,,        Chem.  News,  46.  178. 

ZN.       ,,     ,,     ZIMMERMANN,    ,,        „        ,,        ,,        Ber.  15.  849. 


§26]  ATOMS  AND   MOLECULES.  51 

26.  The  preceding  table  contains  the  names  of  49  ele- 
ments, the  specific  heats  of  which  have  been  directly  deter- 
mined. For  eleven  of  the  remaining  elements  values  have  been 
obtained  which  are  regarded  by  some  chemists  as  representing 
the  specific  heats  of  these  elements  :  the  method  employed  is 
based  on  the  assumption  that  the  molecular  hea?  of  a  solid 
compound  is  equal  to  the  sum  of  the  atomic  heats  of  its 
constituent  elements.  (See  Kopp,  Annalen,  Supplb.  3. 
321 — 339.)  Thus  Kopp  found  the  mean  molecular  heat1  of 
metallic  sulphides  of  the  form  RS  to  be  equal  to  12:  the 
atomic  heat  of  sulphur  is  57 ;  but  12  —  57  =  6-5,  which  num- 
ber is  regarded  as  the  value  of  the  atomic  heat  of  any  one  of 
the  metals  R.  The  mean  value  of  the  atomic  heats  of  these 
metals  found  by  direct  experiment  is  6*4. 

Kopp  has  applied  this  indirect  method  to  calculate  the 
atomic  heats  of  various  elements  with  which  direct  experi- 
ments could  not  be  made2. 

Chlorine :  molecular  heats  of  metallic  haloid  salts : — 
RC1  =12-8     RBr=i3'9    RI  =13-4 
RCl2=i8'5 RI2=i9'4. 

Now  as  (i)  the  atomic  heat  of  each  of  the  metals  R  is 
about  6*4 ;  (2)  the  atomic  heat  of  solid  bromine  and  iodine 
is  about  6*6 ;  (3)  the  chlorides,  bromides  and  iodides 
examined  are  chemically  analogous ;  and  (4)  the  molecular 
heats  of  the  analogous  salts  are  nearly  the  same,  Kopp  con- 
cludes that  the  atomic  heat  of  solid  chlorine  is  about  6*4. 

RC1  (i2-8)-R(6-4)  =  6'4  :    RC12  (18-5)- R  (6-4)  =  12-1,    and    "-=6-05. 

A  further  argument  in  favour  of  this  conclusion  is.  afforded 
by  these  data, 

molecular  heat  of  KC1O3  =  24'8 
„          „         KAsO3=25'3, 

hence  the  atomic  heats  of  arsenic  and  chlorine  are  probably 

1  By  molecular  heat  is  to  be  understood  the  product  obtained  by  multiplying 
the  specific  heat  of  a  compound  into  the  quantity  expressed  by  the   generally 
accepted  formula  of  that  compound ;  the  expression  formula-weight  will  be  em- 
ployed to  signify  this  amount  of  any  compound. 

2  For  detailed  data  see  Kopp,  he.  cit.  p.  293. 

4—2 


52  CHEMICAL  STATICS.  [§  26 

nearly  the  same ;  but  the  atomic  heat  of  arsenic  is  6'i,  there- 
fore the  atomic  heat  of  solid  chlorine  is  probably  about  6'i. 

Fluorine : 

molecular  heat  of  CaF2=  16*4 
atomic  heat  of  Ca=6*8, 

hence  atomic  heat  of  fluorine  =  -  -  =  4-8. 

Nitrogen :  molecular  heats  of  various  more  or  less  analo- 
gous compounds : — 

RC1O3=24'8  RCO3=207 

RAsO3=25'3  RSiO3=2o'5 

RPO3=22'i  RNO3=23'o. 

Hence,  it  is  argued,  the  atomic  heat  of  solid  nitrogen  is 
probably  rather  less  than  that  of  chlorine  or  arsenic  (about  6), 
somewhat  greater  than  that  of  carbon  or  silicon  (about  5*2), 
and  nearly  equal  to  that  of  phosphorus  (about  5  *8) ;  therefore 
the  value  of  the  atomic  heat  of  solid  nitrogen  probably  lies 
between  5*5  and  5 '8. 

Oxygen:  the  molecular  heats  of  metallic  oxides  are,  as  a 
rule,  rather  less  than  those  of  corresponding  haloid  salts  ; 
therefore  the  atomic  heat  of  solid  oxygen  is  probably  less 
than  6 ;  thus 

RO  =iri RC1  =12-8    RBr=i3*9    RI  =13-4, 

RO2=i37 RCl2=i8-6 RI2=i9'4. 

Further  data  for  finding  the  value  sought  for  are  these, 

molecular  heats R2O3=27'2;  KAsO3=25'3;  KC1O4=26'3; 

KMn04=28'3. 

The  values  deduced  for  the  atomic  heat  of  solid  oxygen 
are, 

from  RO  ...4-6,  from  KAsO3...4'2 
„    R0a...37,      „      KC104...3'5   [assuming  Cl  =  6] 
„  R203...4'8,      „    KMn04...3'8, 
hence  the  mean  value  is  4*1. 

Hydrogen :  the  principal  data  are  these, 
molecular  heat  of  ice  (H2O)=9    :  molecular  heat  of  Cu2O  =  i5'6. 

Hence,  it  is  argued,  the  atomic  heat  of  solid  hydrogen  is 
probably  less  than  that  of  copper  by  the  amount  -2—  —  =  3-3  : 


§26]  ATOMS  AND   MOLECULES.  53 

but  atomic  heat  of  copper  =  6'4,  therefore  the  atomic  heat  of 
solid  hydrogen  =  3*1. 

fbut  atomic --heat  of  N1  is  about  5*6) 
Molecular  heat  of  N  H.C1  =  20  :\      .  _., 

land  „  Cl1       „        6'4j 

Now  20—12  =  8,  and  f=2,  therefore  the  atomic  heat  of 
hydrogen  is  about  2. 

Molecular  heat  of  NH4NO3=36'4\ 
„  oxides  R2O3=27'2j  ' 

Hence  36*4  -  27-2  =  9*2,  and  —  =  2-3. 

4 

The  .mean  of  these  three  results  is  2*4,  which  may  perhaps 
be  taken  to  represent  the  atomic  heat  of  solid  hydrogen : 
the  method  of  calculation  however  involves  many  assump- 
tions and  the  use  of  numbers  themselves  obtained  by  indirect 
means.  From  experiments  with  palladium  charged  with  hydro- 
gen, Beketoff  deduced  the  number  5*9  as  representing  the 
atomic  heat  of  solid  hydrogen2. 

The  molecular  heats  of  the  oxides,  chlorides,  carbonates, 
nitrates,  and  sulphates  of  calcium,  barium,  and  strontium  are 
nearly  the  same  as  the  molecular  heats, of  the  corresponding 
salts  of  metals  the  atomic  heats  of  which  have  been  directly 
determined,  and  found  to  be  represented  by  the  mean  number 
6*4;  hence  the  atomic  heats  of  calcium,  barium,  and  strontium 
are  probably  represented  by  a  number  approximately  equal 
to  6-4. 

The  agreement  noticed  between  the  values  of  the  molecular 
heats  of  the  chloride  and  carbonate  of  rubidium,  of  the  oxides 
and  chlorides  of  chromium  and  titanium,  and  of  the  oxides  of 
vanadium  and  zirconium,  and  the  molecular  beats  of  corre- 
sponding salts  of  other  metals  which  themselves  exhibit  the 
mean  atomic  heat  6-4,  shews  that  the  atomic  heat  of  rubidium, 
titanium,  zirconium,  chromium  and  vanadium  is  probably 
about  6'43  (see  notes  6  and  10  to  table  of  specific  heats  of 
elements,  p.  50). 

1  Indirectly  determined,  see  p.  51  and  p.  52. 

2  See  abstract  of  Beketoff 's  paper  (original  is  in  Russian)  in  Ber.  12.  687. 

3  For  a  full  collection  of  specific  heat  data  see  F.  W.  Clarke's  Constants  of 
Nature,  part  n  :  or,  Landolt  and  Bornstein's  Physikalisch-chemische  Tabcllcn. 


54 


CHEMICAL  STATICS. 


[§26 


The  following  numbers  representing  molecular  heats  of 
salts  of  recently  discovered  elements  are  given  by  Nilson 
(Ber.  13.  1459  et  seq.}. 

Temperature. 

Scandium  sails  (80=44-03)   Sc2O3  0*153          o°-ioo° 

Sc2.3S04 
Er203 
Er2.3SO4 
Y203 
Y2.3S04 
Yb203 
Yb2.3SO4 


Erbium  salts  (Er=  166) 
Yttrium  salts  ^=89-5) 
Ytterbium  salts  (Yb  =  i73) 


Specific 
heat. 

0-153 

0-1639 

0-065 

0*104 

O-I026 

0-I3I9 

0-0646 

O-I04 


Molecular 
heat. 

20*8  1 

62*42 
247 


23*3 

6r6 
25-5 
65-8 


Gallium  oxide 
Indium  oxide 


Ga203 
In203 


0-1062 
0*0807 


19-5 

22"2 


If  we  assume  that  the  atomic  heat  of  oxygen  is  4*1  (see 
p.  52),  and  regard  only  the  oxides  in  the  above  table, 
then  the  following  values  are  found  for  the  atomic  heats  of 
the  metals, 


Sc=4'2      Er=6-i 


Yb=6'6  :      Ga=3'6      In=5*o. 


If  a  similar  process  is  applied  to  the  sulphates  (atomic  heat 
of  S=6),  then  the  atomic  heats  of  the  metals  are  all  repre- 
sented by  negative  numbers;  hence  either  (i)  the  value  of 
the  atomic  heat  of  oxygen  in  compounds  is  not  constant,  or 
(2)  that  of  sulphur  varies,  or  (3)  that  of  the  metals  Sc,  Er, 
Y,  Yb,  Ga,  In,  is  negative  in  their  sulphates,  and,  for  some 
of  these  metals,  is  abnormal  in  their  oxides. 

The  last  hypothesis  can  scarcely  be  adopted.  Indeed  if 
the  atomic  heats  of  gallium  and  indium  as  determined  by 
direct  experiment  are  placed  beside  the  numbers  obtained  by 
calculation  from  the  molecular  heats  of  the  oxides  (assuming 
O  =  4'i)  we  have  this  result  : 


Atomic  heat  of  Gallium 
Indium 


Directly 
determined. 

5-4 


Calculated  from 
oxides. 


5-0 


We  can  scarcely  hesitate  which  numbers  to  prefer. 

It  seems  then  that  the  value  to  be  assigned  to  the  atomic 


§  26]  ATOMS   AND   MOLECULES.  55 

heat  of  oxygen  in  oxides1  (and  probably  also  the  value  of  the 
atomic  heat  of  sulphur  in  sulphates)  is  not  a  constant  number, 
but  varies  according  to  the  metal  with  which  the  oxygen  is 
combined2:  but  if  this  is  so,  much  doubt  must  necessarily  be 
thrown  on  the  accuracy  of  the  conclusions  regarding  the 
atomic  heats  of  chlorine,  nitrogen,  and  other  elements,  deduced 
from  the  molecular  heats  of  compounds  of  these  elements. 
It  appears  then  that  the  Garnier-Cannizzaro  generalisation 
(see  ante,  p.  47)  cannot  always  be  applied. 

Although  a  knowledge  of  the  molecular  heats  (so-called) 
of  solid  compounds  may  give  considerable  help  towards  fixing 
the  formulae  of  these  compounds,  and  so,  indirectly,  deciding 
what  multiple  of  the  combining  number  of  an  element  is  to 
be  adopted  as  the  atomic  weight  of  that  element,  yet,  it 
appears  to  me,  that  so  far  as  concerns  the  direct  determination 
of  atomic  weights,  only  those  values  for-  specific  heats  which 
have  been  obtained  by  experiments  on  the  solid  elements 
themselves  are  of  much  value. 

It  is  certain  that  in  some  cases  quite  erroneous  conclusions 
regarding  the  value  of  an  atomic  weight  may  be  deduced 
from  measurements  of  the  specific  heats  of  solid  compounds. 
Thus  it  was  for  some  time  doubtful  whether  the  value  120 
or  240  should  be  assigned  to  the  atomic  weight  of  uranium. 
In  1878  Donath  found  the  specific  heat  of  uranoso-uranic 
oxide  to  be  "0798  (Ber.  12.  742);  assuming  the  specific  heat 

of  solid  oxygen  to  be  0*25    (i.e.  ~J  ,  the  specific   heat   of 

uranium  was  calculated  to  be  '0497  ;  now  '0497  x  120=  5*96, 
therefore  it  was  concluded  by  Donath  that  the  atomic  weight 
of  uranium  is  120.  But  in  1880 — I  pure  uranium  was  pre- 
pared by  Zimmermann  (for  details  see  Ber.  14.  440  and  779 : 
15.  849),  and  the  specific  heat  of  this  metal  was  found  by  him 

1  Such  phrases  as  'atomic  heat  of  oxygen  in  oxides,'  'atomic  heat  of  sulphur 
in   sulphates '   are   perhaps   rather   misleading ;    they   seem    to    assume    that  an 
elementary  atom  has  different  capacities  for  heat  according  to  the  nature  (and 
number)  of  other  atoms  with  which  it  is  combined,  and  that  measurements  of 
these  various  capacities  are  obtainable  ;   this  assumption  is  not,    I   think,   fully 
justified  by  facts. 

2  See  post,  chapter  in.  par.  in.  * 


56  CHEMICAL   STATICS.  [§  2/ 

to  be  '028 ;  but  '028  x  120=  3-3  :  hence,  to  bring  the  atomic 
heat  of  uranium  into  agreement  with  that  of  the  majority  of 
the  elements  it  is  necessary  to  assign  to  the  atomic  weight 
of  this  metal  the  value  240. 

27.  If  the  table  of  maximum  atomic  weights  (p.  45)  is 
compared  with  that  which  gives  the  specific  heats  of  elements 
s(pp.  48 — 49),  it  will  be  found — omitting  the  four  elements 
which  are  placed  in  brackets  in  the  former  table — that  of  the 
34  elements  whose  atomic  weights  have  been  determined  by 
the  application  of  Avogadro's  law,  24  have  also  had  values 
assigned  to  their  specific  heats  by  direct  experiments.  Compar- 
ing the  products  obtained  by  multiplying  the  atomic  weight 
into  the  specific  heat  in  each  of  these  24  cases,  it  is  found  that 
4  of  those  products  fall  below  5 '8  (varying  from  57  to  5*2), 
and  that  20  vary  from  6'8  to  6,  giving  a  mean  value  of 
6'4,  round  which  number  most  of  the  values  are  grouped. 
The  conclusion  to  be  drawn  is  that  the  atomic  heat  of  the 
20  elements  in  question  is  represented  by  the  number  6*4. 
There  are  four  elements  in  brackets  in  the  table  on  p.  45, 
viz.  aluminium,  iron,  copper,  and  gallium :  if  the  maximum 
atomic  weight  of  each,  as  deduced  by  Avogadro's  law,  is 
multiplied  into  the  specific  heat  of  the  element,  the  product 
is  found  to  be  about  12,  but  if  the  true  atomic  weights  are 
assumed  to  be  half  as  large  as  the  numbers  in  the  table,  then 
the  atomic  heat  of  each  of  these  elements  is  represented  by 
the  mean  number  6'4.  Now  there  are  no  valid  reasons 
against  adopting  half  the  maximum  values  obtained  by  Avo- 
gadro's law  as  the  true  values  of  the  atomic  weights  of  the 
four  elements  in  question,  indeed  there  are  strong  chemical 
reasons  in  favour  of  this  course. 

Hence  we  have  a  very  considerable  mass  of  facts  in  favour 
of  the  generalisation, — 

The  atomic  heat  of  all  solid  elements  is  nearly  a  con- 
stant, the  mean  value  being  6*4. 

If  this  be  granted,  we  deduce  the  statement  for  finding 
the  atomic  weight  of  an  element, — 

6'4 

atomic  weight  — ~~ -  , 

spec,  heat 


§  27]  ATOMS  AND   MOLECULES.  57 

provided  always  it  is  remembered  that  the  specific  heat  is 
assumed  to  be  determined  with  the  element  in  the  solid  form, 
and  for  a  considerable  range  of  temperature ;  and  also  that 

the   quotient   - — ~- -  affords  only  an  approximate  value  for 

the  atomic  weight  of  the  element. 

This  method  for  determining  the  atomic  weights  of  ele- 
ments has  been  applied  in  about  20  cases,  besides  those 
cases  where  the  method  of  specific  gravities  has  also  been 
employed  ;  the  numbers  obtained  are  usually  regarded  as  the 
true  atomic  weights  of  the  elements  in  question. 

It  is  evident  that  in  determinations  of  the  specific  heats  of 
solid  elements  we  have  a  most  valuable  means  for  deciding 
which  multiple  of  the  combining  number  of  an  element  is 
to  be  accepted  as  most  probably  expressing  the  value  of 
the  atomic  weight  of  that  element.  When  the  element 
cannot  be  obtained,  or  cannot  be  obtained  in  sufficient  quan- 
tity in  the  solid  form,  then  measurements  of  the  specific  heats 
of  a  series  of  its  solid  compounds  will  afford  more  or  less 
valuable  guidance  in  attempts  to  find  the  atomic  weight  of 
the  element  in  question. 

The  following  statement  fairly  sums  up  the  results  of 
atomic  heat  determinations. 

I.  Solid  elements,  forty-four  in  number,  whose  specific  heats 
have  been  directly  determined,  and  whose  atomic  heats  are  all 
nearly  equal  to  6*4. 

Li  Na  Mg  Al  P  S  K  Ca  Mn  Fe  Co  Ni  Cu  Zn  As 
Se  Br  Zr  Mo  Ru  Rh  Pd  Ag  Cd  In  Sn  Sb  I  Te  La 
Ce  Di  W  Os  Ir  Pt  Au  Hg  Tl  Pb  Bi  Th  U (Cr) 

II.  Solid  elements,  five  in  number,  whose  specific  heats  have 
been  directly  determined,  and  whose  atomic  heats  appear  to  be 
about  5-5. 

Ga  [?  inaccurately  detei.nined]     Be    B     C     Si. 

III.  Solid  elements,  six  in  number,  whose  specific  heats  have 
been  indirectly  determined,  and   whose  atomic  heats  are  pro- 
bably nearly  equal  to  6*4. 

Ca    Ti    V     Rb     Sr     Ba. 


58  CHEMICAL   STATICS.  [§  28 

IV.  Gaseous  elements ;  atomic  heats  very  doubtful,  appa- 
rently variable. 

H    (F)    N    O    Cl. 

Of  the  elements  whose  atomic  heats  are  decidedly  less  than 
6*4,  all,  except  gallium  and  beryllium,  are  nonmetallic  and 
have  atomic  weights  smaller  than  33  :  indeed  if  the  elements 
are  arranged  in  order  of  increasing  atomic  weight,  it  is  found 
that,  with  the  exception  of  lithium,  all  having  an  atomic 
weight  less  than  23  have  also  an  atomic  heat  less  than  6,  and 
that  these  elements,  except  beryllium,  are  nonmetallic. 

28.  The  data  concerning  specific  heats  of  beryllium, 
boron,  carbon,  and  silicon  must  be  examined  in  some  detail. 

Beryllium.  R.  E.  Reynolds  (Phil.  Mag.  (5)  3.  38)  de- 
termined the  specific  heat  of  this  metal  at  100°  to  be  '642  : 
the  metal  used  was  however  impure. 

Nilson  and  Pettersson  (Ber.  11.  351)  determined  the 
specific  heat  of  a  mixture  of  metallic  beryllium  with  known 
quantities  of  beryllium  oxide,  ferric  oxide  and  silica ;  they 
also  determined  the  specific  heat  of  pure  beryllium  oxide, 
and,  the  specific  heats  of  ferric  oxide  and  silica  being  known, 
they  calculated  the  specific  heat  of  the  metal  beryllium  to  be 
•4079,  for  the  temperature  interval  o°  —  100°. 

The  same  chemists  (Ber.  13.  1451  :  see  also  Chem.  News, 
42.  297)  made  a  second  series  of  determinations  with  a 
sample  of  the  metal  containing  only  about  5  per  cent,  of 
beryllium  and  ferric  oxides.  The  following  table  gives  their 
more  important  results : 

Specific  heat  of  Beryllium.    (NiLSON  and  PETTERSSON.) 

Temperature  interval.  Specific  heat.  Sp.  ht.  x  13 '65- 

o°— 46-5°  0-3973  5-4 

o° — 1 00°  0-4246  5 -8 

o°— 214°  0-475  6-4 

o° — 300°  0*5055  6  "9 

Hence  these  chemists  concluded  that  the  atomic  weight 
of  beryllium  ought  to  be  taken  as  I3'65,  and  not  9-1  the 
value  usually  assigned  to  this  constant. 


§  29]  ATOMS  AND   MOLECULES.  59 

The  results  tabulated  above  show  that  the  value  of  the 
specific  heat  of  beryllium  for  the  interval  o°  —  300°  is 

27  per  cent,  greater  than  the  value  for  the  interval  o°  —  50°  ;  is 
7  „  »  »  o°—  200°  ;.  and  is 

19  „  „  „  o°—  100°. 

Using  the  data  of  Nilson  and  Pettersson,  L.  Meyer  (Ber. 
13.  1780),  has  calculated  the  values  of  the  specific  heat  of 
beryllium  at  various  temperatures,  with  the  following  re- 
sults. 

True  specific  heat  of  Beryllium  at  various  temperatures.    (MEYER.) 

y=true  specific  heat  at  temperature  /. 
Ay  =  increase  in  value  of  y  per  i°C. 

Atomic  heat 


20-2° 

0*3973 

O'OOIOI 

3-62' 

5*43 

73*2° 

0*4481 

0*00085 

4*08 

6*12 

157° 

o*5i93 

0*00063 

473 

7*10 

256-8° 

0*5819 

— 

5*29 

8'94 

Hence  it  appears  that  the  specific  heat  of  beryllium 
increases  rapidly  as  temperature  increases,  but  that  the  rate 
of  this  increase  diminishes  :  the  specific  heat  probably  attains 
a  constant  value,  equal  to  about  0*6,  at  300°  or  so1. 

29.  Boron,  Carbon,  and  Silicon.  Very  varying  values 
have  been  obtained  for  the  specific  heats  of  these  three 
elements.  The  following  table  summarises  the  principal 
data  previous  to  the  publication  of  Weber's  papers  [see  Phil. 
Mag.  (4)  49.  161  &  276]. 

Specific  heats  of  Boron,  Carbon,  Silicon.   (Weber's  numbers  not  included.) 
(Temperature  may  be  taken  as  about  35°  —  55°.) 

Sp.  ht.  Sp.  ht.  x  at.  wt.        Observer. 

Boron  —  amorphous  0*254  2  '8  Kp.  1864 

„         crystalline  0*230  2*6                 „  „ 

„                 „  0-252  2-8  M.D.  1873 

,,                 „  0*262  2-9  Rg.  1869 

1  For  a  discussion  of  the  value  to  be  assigned  to  the  atomic  weight  of  beryllium 
see  chapter  in.  par.  in. 


6o 


CHEMICAL  STATICS. 


[§29 


Boron — crystalline 

„          graphitic 
1  Carbon — diamond 

„  gas-carbon 


graphite 


Silicon — fused 


crystalline 


Sp.  ht. 

Sp.  ht.  x  at.  wt. 

Observer. 

0*225 

2'5 

Rg. 

1869 

0-257 

2-8 

„ 

„ 

0-235 

2-6 

„ 

„ 

0-143 

1-7 

B.W. 

1868 

0-147 

r8 

Rg. 

1841 

0*165 

2'0 

Kp. 

1864 

0-186 

2*2 

B.W. 

1868 

0-197 

2'4 

Rg. 

1841 

0-174 

2'I 

Kp. 

1864 

o*i  88 

2*3 

B.W. 

1868 

0*198 

2*4 

Rg. 

1866 

0*138 

3'9 

Kp. 

1864 

0-166 

4*6 

Rg. 

1861 

0*165 

4'6 

Kp. 

1864 

0*171 

4-8 

M.D. 

1873 

0-173 

4'8 

Rg. 

1861 

Weber  (/^.  cit.)  found  that  the  specific  heats  of  carbon, 
boron,  and  silicon  increase  rapidly  as  the  temperature  is 
raised,  but  that  at  high  temperatures  the  velocity  of  the 
increase  becomes  much  smaller.  The  following  table  gives 
a  synopsis  of  Weber's  results : 

Specific  heats  of  Boron,  Carbon,  and  Silicon.     (WEBER.) 

Temp.  Spec.  heat.  Spec.  ht.  X  at.  wt. 

Boron — crystallised  -40°  0-1915 

4-77°  0-2737 

„  «  177°  0-3378 


2-1  1 


372 


233 


0-3663 


These  numbers  show  that  the  specific  heat  of  boron  in- 
creases with  increase  of  temperature,  and  that  the  value  of 
this  increase,  for  a  given  interval,  is  considerably  less  at  high 
than  at  low  temperatures.  The  variations  in  the  rate  of 
this  increase  are  almost  identical  with  the  variations  noticed 
in  the  case  of  carbon  ;  hence  at  temperatures  above  233° 

1  Dewar  {Phil.  Mag.  [4]  44.  461)  found  for  the  specific  heat  of  gas-carbon 
between  20°  and  1040°  the  number  0*32,  for  diamond  the  number  0-366  ;  and 
between  20°  and  a  temperature  estimated  to  be  2000°,  for  'carbon'  the  number 
0-42. 


§  29]  ATOMS   AND   MOLECULES.  6l 

this  identity  will  probably  remain.      Calculated  on  this  as- 
sumption, the  specific  heat  of  boron  at  about  1000°  is  0*50. 

Specific  heats  of  Boron,  Carbon,  and  Silicon.     (WEBER)  continued. 


Carbon — diamond 


graphite 


Porous  wood  carbon 


Temp. 

Spec.  heat. 

-50° 

0-0635 

+  10° 

0-II28 

85° 

0-1765 

250° 

0-3026 

606° 

0-4408 

9850 

0-4589 

-50° 

0-II38 

+  10° 

0-1604 

61° 

0-I990 

201° 

0-2966 

250° 

0-325 

641° 

0-4454 

978° 

0-467 

o°—  23° 

0-1653 

o°—  99° 

0-1935 

o°  —  223° 

0-2385 

Sp.  ht.  x  at.  wt. 
076 

2-12 
3^3 

5-5I 

1*37 

2*39 
3-56 
3'88 

5*35 
5-50 

1-95 
2-07 
2-84 


These  numbers  show  that  the  specific  heat  of  carbon 
increases  from  —  50°  upwards,  the  value  found  at  600°  being 
about  seven  times  as  great  as  that  found  at  —  50° ;  but  that 
the  rate  of  this  increase  is  very  small  at  high  temperatures, — 
from  a  red  heat  upwards  the  rate  is  about  one-seventeenth 
of  that  from  o°  to  100°. 

The  specific  heats  of  diamond  and  graphite  differ  at  tem- 
peratures below  about  6co°,  but  from  this  point  upwards  they 
are  practically  identical ;  the  numbers  given  for  porous  wood 
carbon  are  almost  the  same  as  those  for  graphite  at  the  same 
temperature-intervals,  hence  it  may  be  said  that  at  high 
temperatures  (above  600°)  the  various  modifications  of  carbon 
have  probably  all  the  same  specific  heat. 


Table  continued. 


Silicon — crystallised 


Temp. 

Spec.  heat. 

Sp.  ht.  X  a 

-40° 

OT36 

3'8l 

+  57° 

0-I833 

S'l3 

128° 

0-196 

5-50 

184° 

0'20I  I 

5-63 

232° 

O-2029 

5-68 

62 


CHEMICAL   STATICS. 


[§30 


The  specific  heat  of  silicon  attains  an  almost  constant 
value  at  about  200°. 

30.  It  is  evident  that  the  specific  heat  of  an  elementary 
body  is  not  a  constant  number,  but  varies  with  the  tem- 
perature, and  that  the  relation  between  the  variation  of 
specific  heat  and  that  of  temperature  differs  for  each  element. 
The  following  formulae  calculated  from  experimentally  deter- 
mined numbers,  express  the  relation  in  question  for  some  of 
the  elements. 


1  Carbon — diamond  sp.  ht.= 0*4408 +0*0000405  /,  where  /  varies  from 

6oo°— 800' 

„      „     „  =0*4408  +  0*000056  it  „ 

„    graphite   „  =0*4454  + 0*0000472  /  „ 

„      „     „  =0*4454  + 0*0000840  /  „ 

„  =  0*0910  +  0*000023  /  „ 

„  =0*0865+  0*000044 1  „ 

„  =  0*02  86 +  0*00001 9  /  „ 

„  =0*031 7  + 0*000006  /  „ 

„  =  0*031 7  + 0*000006  /  „ 

„  =0*1053  +  0*000071  /'  „ 

„  =0*050  +0*000044  /  „ 

„  =0*0466+ 0*000020  /  „ 

„  =0*0269  + 0*000020  /  „ 


2  Copper 
2  Zinc 

2  Lead 

3  Platinum 
3  Iridium 

2  Iron 
2  Tin 

2  Antimony 
2  Bismuth 


800°  —  1000° 
6oo°—  800° 
800°  —  1000° 
o°  —  250° 


0—  1200 


o°  —  250° 


The  specific  heat  of  any  substance  also  varies  with  varia- 
tions in  the  physical  state  of  that  substance  —  thus  : 


Bromine — solid     ... 

„          liquid  ... 
Soft  copper 
Hard  copper 
Iron  sulphide  as  strahlite 
„  pyrites  . 

Chlorine — solid     ... 

„         4  gaseous 
Mercury — solid     ... 


Sp.  heat. 
0*0843 
0*1110 
0*0948 
0*0934 


Mercury — 4  gaseous 

Soft  steel 

Hard  steel 

Titanium  oxide  as  rutile ... 
„  brookite 

„          artificial    ... 
Calcium  carbonate  as  calc- 
spar     ... 
,,          as  arragonite 


Sp.  heat. 
0*OI5 
O*Il65 
0*1175 

o*i  666 
0*1610 
0*1716 


0*1279 

0*180 

0*093  sFar 0*205 

0*032  „          as  arragonite    0*204 

The  specific  heats  of  the  elementary  bodies  have  gener- 
ally been  determined  at  temperatures  situated  at  very  varying 

1  Weber  (loc.  cit.}. 

2  Bede,  Mem.  Conronn.  de  FAcad.  Brux.  27.  3  (1855). 

3  Violle,  Compt.  rend.  85.  543. 

4  Calculated  for  constant  volume. 


§§30^30  ATOMS   AND   MOLECULES.  63 

intervals  from  the  melting  points  of  these  elements ;  the 
physical  aggregation  of  the  specimens  examined  has  also 
varied  much  ;  hence  the  values  found  for  the  specific  heats 
of  the  elements  cannot  be  regarded  as  strictly  comparable. 

There  appears  to  be  a  certain  interval  of  temperature 
within  which  the  value  of  the  specific  heat  of  an  element 
becomes  nearly  constant,  and  for  this  interval  only  can  the 
element  be  said  approximately  to  obey  the  law  of  Dulong 
and  Petit,  as  stated  on  p.  56.  This  temperature-interval 
varies  for  each  element,  especially  for  the  nonmetallic  ele- 
ments with  small  atomic  weights ;  for  many  elements  it  may 
be  roughly  taken  as  from  o°  to  100°. 

Kopp  (loc.  cit.)  has  supposed  that  the  atoms  of  certain 
elements — more  especially  of  boron,  carbon  and  silicon — are 
built  up  of  simpler  parts,  have  themselves  a  grained  struc- 
ture, and  that  at  high  temperatures  the  atoms  of  these 
elements  are  composed  of  a  smaller  number  of  those  little 
parts  than  at  lower  temperatures.  Heat  added  at  low  tem- 
peratures is  supposed,  on  this  hypothesis,  to  be  used  in  sepa- 
rating the  atomic  groups.  Kopp's  hypothesis  will  be  again 
referred  to  in  the  chapter  on  the  nature  of  the  elements ; 
meanwhile  it  may  be  observed,  that  the  facts  of  spectroscopy 
seem  to  point  to  the  existence  of  a  more  complex  structure  in 
the  nonmetallic  than  in  the  metallic  molecules  ;  that  allo- 
tropy  occurs  markedly  only  among  the  nonmetals ;  that 
the  molecules  of  the  two  metallic  elements  whose  vapour- 
densities  have  been  determined  are  monatomic ;  that  the 
atomic  heat  of  tellurium,  a  metal-like  nonmetal  belonging 
to  the  oxygen  group,  is  6'O,  of  the  less  metal-like  selenion 
about  5 -8,  of  the  decidedly  nonmetallic  sulphur  about  5*5, 
and  of  the  typical  nonmetal  oxygen  probably  not  more 
than  4  ;  and  finally  that  the  molecular  structures  of  oxygen, 
sulphur,  and  selenion  vapours  are  more  complex  than  that 
of  tellurium  vapour. 

31.  A  consideration  of  the  data  which  has  been  sum- 
marised in  the  preceding  paragraphs  shews,  I  think,  that  the 
application  of  Avogadro's  law  is  of  more  value  to  the  chemist 
as  a  means  of  determining  the  atomic  weights  of  elements, 


64  CHEMICAL   STATICS.  [§  31 

than  the  law  of  Dulong  and  Petit.  From  a  general  considera- 
tion of  the  molecular  theory  of  matter  it  is  also  apparent  that 
a  deduction  which  does  not  necessitate  an  exact  hypothesis 
as  to  the  internal  structure  of  molecules  is  more  trustworthy 
and  more  appropriate,  in  the  present  state  of  knowledge,  than 
another  which  does  necessitate  some  such  hypothesis. 

The  molecular  explanation  of  the  gaseous  laws  expressing 
relations  between  volume,  pressure  and  temperature,  and  of 
Avogadro's  law,  may  be  considered  as  fairly  complete ;  but 
in  order  to  explain  the  law  of  molecular  specific  heats  more 
knowledge  of  the  internal  structure  of  molecules  than  we  now 
possess  is  necessary1.  For  the  specific  heat  of  a  substance 
depends  on  the  rate  at  which  the  whole  energy  of  the  mole- 
cule increases  with  increase  of  temperature :  but  this  energy 
is  made  up  of  two  parts,  (i)  the  energy  of  agitation,  that  is, 
the  energy  the  molecule  would  possess  if  it  moved  as  a  whole 
with  the  motion  of  its  centre  of  mass,  or  in  other  words 
without  rotation  ;  and  (2)  the  energy  of  rotation,  that  is,  the 
energy  the  molecule  would  possess  if  its  centre  of  mass  were 
reduced  to  rest,  in  other  words  the  energy  due  to  the  motion 
of  the  parts  relatively  to  the  centre  of  mass  of  the  molecule2. 
If  it  is  assumed  that  the  energy  due  to  the  rotational  motions 
of  the  parts  of  the  molecule  tends  towards  a  value  having  a 
constant  ratio  to  the  energy  of  agitation  of  the  molecule, 
then  a  simple  expression  is  found  for  the  whole  energy ;  but 
this  expression  contains  a  factor  which  varies  in  different 
gases,  and  the  value  of  which  has  been  determined  only  in  a 
few  cases3.  And  moreover  it  is  probable  that  when  the  energy 
due  to  the  rotational  motions  of  the  parts  of  a  molecule 
becomes  greater  than  a  certain  quantity,  the  molecule  separates 
into  parts ;  hence  when  heat  is  imparted  to  a  mass  of  mole- 
cules work  is  probably  in  many  cases  done  in  destroying 
some  of  the  molecules  as  such4.  Hence  the  molecular  expla- 

1  Clerk  Maxwell,  C.  S.  Journal  [2]  13.  507. 

2  Clerk  Maxwell,  loc.  cit.  p.  502. 

3  See  Clerk  Maxwell's  Heat,  pp.  317—319  (6th  ed.). 

4  See  Hicks,  Phil.  Mag.  (5).  4.  80,  and  174.     'On  some  effects  of  Dissocia- 
tion on  the  Physical  Properties  of  Gases.' 


§  32]  ATOMS   AND   MOLECULES.  65 

nation  of  specific  heat  is  not  at  present  in  so  advanced  a  state 
as  that  of  the  relations  between  the  volumes,  pressures  and 
temperatures  of  gases1. 

32.  The  so-called  'law  of  isomorphism'  affords  a  basis 
on  which  is  founded  another  method  for  determining  the 
atomic  weights  of  elementary  substances. 

The  Abbe  Haiiy,  whose  views  were  dominant  in  crystal- 
lography in  the  early  days  of  this  century,  admitted  a  close 
connection  between  crystalline  form  and  chemical  compo- 
sition, but  he  thought  that  each  chemically  distinct  body 
must  be  characterised  by  a  definite  and  peculiar  form. 

In  1816  Gay-Lussac  noticed  that  the  growth  of  crystals 
of  potash  alum  was  not  affected  by  placing  them  in  a  solution 
of  ammonia  alum. 

Various  observations  of  this  kind  were  made  from  time  to 
time2  until  1819,  when  E.  Mitscherlich  propounded  the  law  of 
isomorphism,  which,  modified  and  developed,  was  stated  by 
him  in  1821  in  the  following  terms  :  '  Equal  numbers  of  atoms 
'  similarly  combined  exhibit  the  same  crystalline  form ;  identity 
'  of  crystalline  form  is  independent  of  the  chemical  nature  of 
'  the  atoms,  and  is  conditioned  only  by  the  number  and  con- 
'  figuration  of  the  atoms.' 

Since  this  date  various  observers  have  advanced  the  know- 
ledge of  the  relations  between  crystalline  form  and  chemical 
composition3.  The  more  important  generalisations  are  as 
follows. 

Similar  atomic  structure  is  not  necessarily  accompanied 
by  identical  crystalline  form  ; 

e.g.  PbCrO4  monoclinic,  and  PbMoO4  quadratic  ; 
AgCl  and  AgBr  regular,  and  Agl  hexagonal ; 

KNO3    and    (NH4)NO3   rhombic   but   not   identical,    CsNO3    and 
RbNO3  hexagonal. 

1  See  in  connection  with  this  subject  Strecker,     Wied.   Ann.    13.   20;    and 
Boltzmann,  do.  13.  544:  and  18.  309. 

2  For  a  full  historical  account  of  the  development  of  the  conception  of  Iso- 
morphism, with   copious  references,  see  the  article  '  Isomorphie '  in  the  Neucs 
Handworterbuch  der  Chemie,  Bd.  ill.  p.  844  et  scq. 

3  See  especially  Handworterbuch,  loc.  cit.  and  Kopp's  Lehrbuch  der  physikal- 
ischen  und  theoretischen  Chemie  (and  Ed.),  Bd.  n.  pp.  136 — 155. 

M.  C.  5 


66  CHEMICAL  STATICS.  [§  32 

Unlike  atomic  structure  may  be  accompanied  by  similar 
or  identical   crystalline  form :    thus  Marignac1   shewed   that 
the  following  salts  crystallise  in  identical  forms  ; — 
K2TiF6.H2O,  K2NbOF5.H2O,  K2WO2F4 .  H2O, 
CuTiF6.4H2O,  CuNbOF5  .  4H2O,  CuWO2F4 .  4H2O. 

In  these  salts  we  must  suppose  isomorphism  to  occur 
between  certain  groups,  e.g.  TiF2,  NbOF,  and  WO,,.  The 
isomorphism  of  potassium  and  ammonium  salts  shews  that 
the  atom  K  is  crystallographically  equivalent  to  the  group 
of  atoms  NH4. 

The  form  of  the  constituents  of  isomorphous  compounds 
cannot  always  be  deduced  from  that  of  the  compounds  them- 
selves ;  e.g.  manganous  and  manganic  sulphides  crystallise  in 
regular,  but  sulphur  in  rhombic  or  monoclinic  forms,  therefore 
manganese  does  not  necessarily  crystallise  in  regular  forms. 
So  also  the  sulphates  of  nickel,  magnesium  and  zinc  crystallise 
in  rhombic  forms,  but  the  oxides  of  nickel  and  magnesium 
in  regular,  and  oxide  of  zinc  in  hexagonal  forms.  Again, 
arsenic  usually  crystallises  in  rhombic  forms,  the  crystals  of 
phosphorus  belong  to  the  regular  system,  yet  the  analogous 
compounds  of  these  elements  are  generally  isomorphous, 
Kopp  generalises  such  facts  as  these  in  the  following  state- 
ment : — '  Bodies  possessing  the  same  crystalline  form  combine 
'  in  fixed  proportions  to  form  crystals  whose  form  is  indepen- 
'  dent  of,  and  often  different  from,  that  of  their  constituents.' 

In  other  cases  the  constituents  of  isomorphous  bodies  are 
themselves  isomorphous,  e.g.  the  compound  3Ag2S  .  Sb2S3  has 
the  same  crystalline  form  as  the  compound  3Ag2S .  AsaS3, 
Sb2S3  and  As2S3  are  isomorphous  in  rhombic  forms,  and 
arsenic  and  antimony  form  almost  identical  rhombic  crystals. 
Hence  we  must  distinguish  strict  isomorphism  as  applied  to 
bodies  which,  with  similar  composition,  exhibit  the  same  or 
nearly  the  same  crystalline  form ;  and  isomorphism  as  more 
loosely  applied  to  bodies  which,  although  not  themselves 
crystallising  in  the  same  form,  nevertheless  combine  with 
other  bodies  to  produce  strictly  isomorphous  compounds  into 
which  they  enter  as  corresponding  groups2. 

1  Ann.  Chim.  Phys.  60.  257.  2  Kopp,  Lehrbuch,  &c.  loc.  cit. 


§§  32,  33]  ATOMS   AND   MOLECULES.  67 

A  certain  latitude  is  generally  allowed  in  the  application 
of  the  term  '  truly  isomorphous  crystals.'  This  latitude  has 
gradually  been  more  and  more  advanced  until  it  has  be- 
come difficult  to  give  an  exact  meaning  to  the  expression. 
The  measurements  of  the  angles  of  two  salts  are  some- 
times identical1 ;  chemically  analogous  compounds  sometimes 
crystallise  in  forms  closely  resembling  one  another,  yet  be- 
longing to  different  systems2;  salts  with  identical  crystalline 
form  sometimes  exhibit  optical  differences3.  Are  all  such 
salts  to  be  called  truly  isomorphous  ?  Kopp4  proposes  that 
only  those  salts,  any  one  of  which  is  capable  of  growing  in 
unmodified  form  when  immersed  in  a  solution  of  any  other, 
should  be  regarded  as  strictly  isomorphous. 

It  would  appear  that  all  the  constituents  of  a  compound 
exert  an  influence  on  the  form  of  that  substance.  Isomorphism 
may  not  be  exhibited  in  comparatively  simple  compounds  of 
two  elements,  but  may  appear  in  more  complex  compounds 
of  the  same  elements  ;  e.g.  many  of  the  simpler  compounds  of 
cadmium  are  not  isomorphous  with  the  analogous  compounds 
of  the  metals  of  the  magnesium  group  (Mg,  Mn,  Fe,  Co,  Ni, 
Zn,  Cu,  Ca),  but  comparatively  complex  cadmium  salts — such 
as  CdSO4.  K2SO4.6H2O — are  generally  isomorphous  with  the 
corresponding  compounds  of  those  metals.  So  many  simple 
salts  of  sodium  and  potassium  are  not  isomorphous,  although 
their  composition  is  similar,  but  the  alums  are  isomorphous. 

One  may  suppose  that  the  presence  of  a  large  number  of 
isomorphous  atoms  exerts  a  dominating  influence  over  a 
smaller  number  of  non-isomorphous  atoms. 

33.  As  we  know  the  crystalline  form  of  comparatively 
few  elements5,  the  statement  that  such  or  such  elements  form 
an  isomorphous  group,  generally  means  only  that  the 
analogous  compounds  of  these  elements  are  for  the  most  part 
isomorphous. 

For  examples  see  Roscoe  and  Schorlemmer's  Treatise,  I.  742. 
See  Marignac,  Ann.  Min.  [5]  9.  and  15.  &c. 
See  Baker,  C.  S.  Journal  Trans,  for  1879.  760. 
Ber.  12.  900  et  seq. 

See,  for  crystalline   forms  of  elements   in   free   state,  Watts's   Dictionary^ 
vol.  in.  p.  429. 

^> 

- 


68  CHEMICAL   STATICS.  [§33 

The  more  important  groups  of  isomorphous  elements,  as 
thus  understood,  are  as  follows1 : 

GROUP  I.     Fluorine,  Chlorine,  Bromine,  Iodine,  \Cyanogen\-,  in  all 
compounds  : 

partially  Manganese;  in  compounds  of  the  type  RMnO4. 

GROUP  II.     Sulphur,  Selenion;  in  all  compounds  and  as  elements  in 
monosymmetric  forms  : 

partially  Tellurium;  in  compounds  of  the  type  R"Te  : 

„         Chromium,  Manganese,  Tellurium;  in  salts  of  their  acids 

belonging  to  type  H2SO4  : 
„        Arsenic,  Antimony;  in  compounds  of  the  type  R/'S^ 

GROUP  III.     Arsenic,  Antimony,  Bismuth,  Tellurium;  as  elements, 
and  the  three  first-named  in  all  corresponding  compounds  : 

partially  Phosphorus  and  Vanadium;  in  salts  of  their  acids  : 

„        Nitrogen  with  Phosphorus,  Arsenic,  Antimony;  in  organic 
bases. 

GROUP  IV.     Lithium,  Sodium,  Potassium,  Rubidium,  Casium,  {Am- 
monium} ;  in  most  compounds  : 

partially  Thallium ;  in  some  compounds  : 

„        Silver,  in  some  compounds  (especially  with  sodium}. 

GROUP  V.     Calcium,  Strontium,  Barium,  Lead ;  Magnesium,  Zinc, 
Manganese,  Iron;  e.g.  in  carbonates  : 

partially  Nickel,  Cobalt,  Copper ;  with  iron  in  some  compounds,  e.g. 

sulphates  : 
„        Lanthanum,  Cerium,  Didymium,   Yttrium,  Erbium;  with 

calcium,  in  compounds  of  type  R"O : 
„         Copper,  Mercury ;  with  lead,  in  oxy-compounds: 
„        Beryllium,   Cadmium,  Indium ;   with  zinc,  in  some  com- 
pounds : 

„         Thallium;  with  lead,  in  some  compounds. 
GROUP  VI.  Ahuninium,  Chromium,  Manganese,  Iron;  in  the  sesqui- 
oxides  [R2O3]  and  salts  derived  therefrom  : 

partially  Ceritim,  Uranium ;  in  their  sesquioxides. 

GROUP  VII.     Copper,  Silver;  in  compounds  of  the  type  (R2)"O  : 
partially  Gold;  with  silver. 

GROUP  VIII.    Ruthenium,  Rhodium,  Palladium,  Iridium,  Platinum, 
Osmium;  in  most  compounds: 
partially  Iron,  Nickel,  Gold: 
„         Tin  \?  Tellurium~\. 

1  From  article  '  Isomorphie '  in  Nettes  Hanfavorterlnich,  loc.  cit. 


§§  34>  35]  ATOMS   AND   MOLECULES.  69 

GROUP  IX.     Carbon,  Silicon,  Titanium,  Zirconium,  Tin,  Thorium; 
partially  in  compounds  of  the  type  RO2,  and  salts  derived  from  the 
type  H2RO3  :  carbon  with  silicon  in  many  correspond- 
ing so-called  organic  compounds. 
„        Iron ;  with  titanium. 

GROUP  X.     Niobium,  Tantalum  ;  in  all  their  compounds. 
GROUP  XI.     Molybdenum,  Tungsten;  in  all  their  compounds : 
partially  Chromium;  in  salts  of  acids  of  the  type  H2RO4. 

34.  The  terms  dimorphous,  trimorphous,  polymorphous  were 
used  by  Mitscherlich.      Many  examples  of  the  phenomena  to 
which  these  names  are  applied  are  now  known:  thus  calcium 
carbonate  crystallises  in  hexagonal  forms  as  calcspar,  and  in 
rhombic  forms  as  arragonite :    titanium  oxide  assumes  two 
distinct  quadratic  forms,  one  being  known  as  rutile  the  other 
as  anatase,  and  also  crystallises  in  brookite  as  rhombic  prisms: 
arsenious  oxide  crystallises  in  octahedral,  antimonious  oxide 
in    rhombic   forms,   but    if    amorphous    arsenious    oxide    is 
heated  in  a  sealed  tube  so  that  one  part  of  the  tube  is  at  400° 
and  the  rest  below  this  temperature,  the  oxide  deposited  in 
the  middle  part  of  the  tube  is  found  to  be  isomorphous  with 
rhombic  antimonious  oxide;  the  latter  oxide  is  also  known  in 
octahedral  forms,  so   that  the  isodimorphism   of  these   two 
oxides  is  complete. 

35.  If  it  is  assumed  that,  as  a  general  rule,  those  amounts 
of  two  substances  which  are  crystallographically  equivalent 
have   analogous    atomic    constitutions;    and    if  we   suppose 
that  of  two  compounds  exhibiting  identical  crystalline  form 
the  atomic  weights  of  the  elements  in  one  are  known,  it  is 
evident  in  what  way  determinations  of  crystalline  form  may 
aid  in  fixing  atomic  weights. 

To  take  an  example : — from  determinations  of  the  specific 
gravities  of  gaseous  compounds  and  analyses  of  these  com- 
pounds, the  value  52*4  is  assigned  to  the  atomic  weight  of 
chromium  ;  this  number  is  verified  by  measurements  of  the 
specific  heat  of  the  same  metal ;  the  formula  «Cr2O3  is  hence 
assigned  to  the  green  oxide  of  chromium.  But  this  oxide 
exhibits  the  same  crystalline  form  as  ferric  oxide,  hence  the 
latter  oxide  should  probably  be  represented  by  the  formula 


70  CHEMICAL   STATICS.  [§35 

?zFe2O3 ;  as  this  formula  is  quite  in  keeping  with  analyses  it  is 
assigned  to  ferric  oxide.  On  comparing  these  crystallograph- 
ically  equivalent  quantities  of  the  two  oxides  it  is  found 
that  52*4x2  parts  of  chromium  are  replaced  by  5  5 '9x2  parts 
of  iron,  but"  as  52*4  has  been  determined  to  be  the  atomic 
weight  of  chromium  it  is  argued  that  the  atomic  weight  of 
iron  is  represented  by  the  number  55*9.  As  the  specific  heat 
of  iron  multiplied  into  55-9  gives  the  product  6 '4,  55-9  is 
almost  certainly  the  true  atomic  weight  of  iron.  Again,  the 
formulae  of  potassium  perchlorate  and  permanganate  were 
at  one  time  written  KO  .  C1O7  and  KO  .  Mn2O7.  Berzelius 
proposed  the  formulae  KO  .  C1O7  and  KO  .  MnO7,  which  on  the 
system  of  notation  now  adopted  became  KC1O4  and  KMnO4 
respectively :  these  formulae  represent  crystallographically 
equivalent  quantities  of  the  two  salts  ;  if  it  is  assumed  that 
Cl  represents  the  weight  of  the  atom  of  chlorine  (35*37),  then 
Mn  (55)  probably  represents  the  weight  of  the  atom  of 
manganese. 

Observations  of  crystalline  form  have  sometimes  led  the 
way  to  correct  determinations  of  atomic  weights  or  to  changes 
in  the  received  values  of  such  weights.  Thus  H.  Rose1  gave 
the  name  of  hyponiobium  to  a  supposed  allotropic  form  of 
the  metal  niobium ;  but  Marignac2  shewed  that  compounds 
of  the  hypothetical  metal  were  identical  in  crystalline  form 
with  certain  compounds  of  tin  and  titanium,  and  concluded 
that  Rose's  hyponiobium  was  itself  isomorphous  with  the 
atomic  groups  SnF  and  TiF,  and  was  therefore  probably  a 
compound.  Further  experiments  shewed  that  the  hypo- 
niobium  of  Rose  was  really  composed  of  niobium  and  oxygen 
in  the  proportions  expressed  by  the  formula  NbO,  provided 
that  this  group  was  regarded  as  crystallographically  equivalent 
to  SnF  and  TiF ;  if  this  were  admitted  it  followed,  from  the 
.analyses  of  the  various  compounds,  that  one  atom  of  tin  or 
titanium  (117*8  or  48  parts  by  weight  respectively)  was  re- 
placed by  94  parts  by  weight  of  niobium,  and  that  this  number 
therefore  represented  the  weight  of  the  atom  of  niobium3. 

1  Fogg.  Ann.  108.  273.  2  Ann.  Chim.  Phys.  60.  257. 

3  Marignac's  conclusions  were   afterwards  confirmed   by  determinations,  by 


§  36]  ATOMS  AND   MOLECULES.  71 

The  facts,  of  which  an  outline  has  been  given,  shew  that 
until  more  extended  and  precise  knowledge  of  the  law  ex- 
pressing the  connections  between  crystalline  form  and  chemi- 
cal constitution  is  obtained,  that  method  for  determining  the 
atomic  weights  of  elements  which  is  founded  on  these  connec- 
tions can  be  applied  only  tentatively  and  in  a  limited  number 
of  cases.  The  method  may  however  now  be  of  considerable 
service  in  suggesting  lines  of  research  bearing  on  the  problems 
connected  with  atomic  weight  determinations. 

It  appears  probable  that  the  crystalline  form  of  a  sub- 
stance is  connected  at  once  with  the  internal  structure  of  the 
molecules  of  the  substance  and  with  the  configuration  of  the 
molecules  themselves.  No  attempt  has  been  made,  nor  can 
in  the  present  state  of  knowledge  hopefully  be  made  in  any 
but  the  broadest  manner,  to  apply  to  the  facts  of  crystallog- 
raphy the  dynamical  theory  of  the  molecular  structure  of 
matter. 

36.  I  have  endeavoured  to  shew  that  the  most  trust- 
worthy method  for  determining  molecular  and  atomic  weights 
is  founded  on  Avogadro's  law,  which  is  itself  an  outcome  of 
the  application  of  dynamical  reasoning  to  a  physical  theory. 
Formerly  it  was  supposed  that  strictly  chemical  evidence 
must  be  of  paramount  importance  in  determining  these  quan- 
tities. Although  the  superior  importance  of  Avogadro's  law 
is  now  admitted,  this  law  can  only  be  applied  to  a  limited 
number  of  substances,  hence  we  are  frequently  obliged  to 
have  recourse  to  purely  chemical  evidence  in  support  of  this 
or  that  molecular  weight.  The  nature  of  this  evidence  must 
now  be  shortly  illustrated. 

In  1850  Brodie1  endeavoured  to  shew  that  there  exists  no 
difference  of  kind  between  those  reactions  wherein  elementary 
bodies  are  produced,  or  react,  and  those  in  which  compound 
bodies  are  alone  concerned.  He  supposed  that  the  small 

Deville  and  Troost,  of  the  specific  gravity  of  gaseous  chloride  and  oxychloride  of 
niobium:  see  Compt.  rend.  60.  1221. 

Roscoe's  researches  on  the  atomic  weight  of  vanadium  afford  a  very  in- 
structive example  of  the  employment  of  the  results  of  crystallographic  measure- 
ments in  fixing  atomic  weights.  Phil.  Trans,  for  1868,  I.  et  seq. 

1  Phil.  Trans,  for  1850,  759,  and  also  C.  S.  Journal,  4.  194. 


72  CHEMICAL   STATICS.  [§  36 

particles  of  elementary  substances  set  free  during  reactions, 
or  taking  part  in  reactions,  are  composed  of  smaller  parts 
which  exhibit  certain  mutual  polar  relations.  Silver  chloride 
is  not  decomposed  by  oxygen,  but  it  is  readily  acted  on 
by  potassium  oxide  with  production  of  silver  oxide  and 
potassium  chloride  ;  hydriodic  and  iodic  acids  decompose 
one  another  with  production  of  free  iodine;  silver  oxide 
decomposes  hydrogen  peroxide  to  form  silver,  water,  and  free 
oxygen,  half  of  the  oxygen  coming  from  the  silver  oxide  and 
half  from  the  peroxide  ;  iodine  decomposes  barium  peroxide 
with  production  of  barium  iodide  and  oxygen.  These  re- 
actions were  thus  written  by  Brodie  (translating  into  the  new 
notation)  : 

(i)  ~ 


(+and 

(2) 


(3) 
(4) 

That  part  of  Brodie's  hypothesis  which  supposed  a  polar 
condition  of  atoms  in  molecules  was  not  generally  adopted 
by  other  chemists,  but  it  was  admitted  that  his  researches 
established  a  general  similarity  of  function  and  composition 
between  elementary  and  compound  molecules. 

In  the  same  year  Williamson1  distinguished  between  the 
atom  of  zinc  in  combination,  and  the  free  metal  zinc  (that  is 
to  say,  he  recognised  that  the  atom  of  an  element  is  not 
possessed  of  the  same  properties  as  the  molecule  of  that 
element)  :  he  said  it  is  not  quite  accurate  to  speak  of  '  zinc  ' 
as  existing  in  zinc  sulphate. 

Recognising  then  that  chemical  reactions  took  place  be- 
tween molecules,  chemists  defined  the  molecule  as  the  smallest 
part  of  a  substance  capable  of  taking  part  in  a  chemical 
change,  or  as  the  acting  chemical  unit.  Supposing  the  atomic 
weights  of  the  elements  forming  a  compound  to  be  known, 
the  best  method  of  determining  the  molecular  weight  of  the 
compound  appeared  to  be  to  find  that  formula  which  should 
express  the  atomic  constitution  in  the  simplest  manner. 

1  C.  S.  Journal,  4.  355. 


§  36]  ATOMS   AND   MOLECULES.  73 

Thus  hydrogen  and  nitrogen  are  combined  in  ammonia  in 
the  proportion  of  3  parts  by  weight  of  the  former  to  14  of 
the  latter ;  assuming  the  atomic  weights  of  these  elements  to 
be  I  and  14  respectively,  the  atomic  composition  of  am- 
monia may  be  represented  by  the  formula  NH3;  and  as  the 
reactions  in  which  this  substance  takes  part  might  all  be 
represented  as  involving  17,  or  a  whole  multiple  of  17 
parts  by  weight  of  this  compound,  and  moreover  as  the 
hydrogen  in  17  parts  by  weight  of  ammonia  was  demonstrably 
divisible  by  chemical  reactions  into  3  parts,  17  was  taken 
as  the  molecular  weight  of  ammonia.  An  instructive  illus- 
tration of  this  method  of  fixing  a  minimum  molecular  weight 
is  furnished  by  Williamson's  famous  researches  on  ethers1. 
The  formulae  generally  adopted  for  common  alcohol  and 
ether,  previous  to  Williamson's  work,  were  C4H6O2  and 
C4H5O  respectively  (C  =  6  ;  O  =  8).  Williamson  allowed 
ethylic  iodide  to  react  on  potassium  alcoholate,  expecting 
that  ethylated  alcohol  would  be  produced, — thus  C4H5KO2 
+  C4H5I  should  give  C4H6(C4H5)O2  +  KI,— but  the  product  was 
ordinary  ether.  If  the  generally  accepted  formula  for  ether 
were  doubled  the  reaction  would  be  explained,  and  ether 
would  be  regarded  as  an  oxide  of  ethyl  (C4H5)2O2.  Again, 
Williamson  found  that  when  sulphuric  acid  acts  on  ethylic 
alcohol,  and  methylic  alcohol  is  added  to  the  mixture,  a 
single  substance  having  the  properties  of  an  ether,  and  the 
formula  C3H4O  or  a  whole  multiple  of  this,  distills  over :  if 
the  formula  of  ether  is  C4H5O,  then  that  of  methylic  ether  is 
C2H3O,  and  a  mixture  of  these  ought  to  be  obtained  in  the 
reaction  just  mentioned;  but  if  ether  is  (C4H5)2O2  then  the 
single  ether  obtained  is  probably  methyl-ethyl  oxide,  i.e. 
C4H6(C2H3)O2  (  =  2C3H4O)2.  Thus  was  shewn,  on  purely 
chemical  grounds,  the  necessity  of  doubling  the  generally 
accepted  molecular  formula  for  ether. 

No  purely  chemical  method  has  been  found  for  deter- 
mining molecular  weights  which  is  capable  of  general  appli- 
cation ;  each  compound  must  be  considered  as  a  separate 

1  See  C.  S.  Journal,    4.  106  and  229. 

3  Translated   into    modern   notation,   these  formulae  become  (C2H5)2O   and 
C2H5(CH3)O  respectively. 


74  CHEMICAL   STATICS.  [§  36 

problem.      The   more   important   methods  may  however  be 
roughly  classified. 

There  is  the  method  of  analogies,  which  is  well  illustrated 
by  the  example  of  ether  already  considered.  The  smallest 
amount  of  sulphuretted  hydrogen  which  takes  part  in  chemi- 
cal changes  is  represented  by  the  formula  H2S  (assuming 
S  =  32)  the  hydrogen  in  this  compound  is  replaceable  in  two 
parts — with  production  of  KHS  and  KKS — hence  the  mole- 
cular formula  is  not  less  than  H2S.  But  compounds  of  selenion 
and  tellurium  with  hydrogen,  analogous  in  general  properties 
to  sulphuretted  hydrogen,  are  known  ;  from  the  marked 
similarity  between  these  two  elements  and  sulphur  it  is  very 
probable  that  the  molecular  formulae  of  the  two  compounds  in 
question  are  H2Se  and  H2Te  respectively :  as  these  formulae 
satisfy  the  analytical  numbers,  they  may  be  adopted.  But  if 
similar  reasoning  is  applied  to  the  cases  of  aluminum  and 
indium — metals  which  are  closely  related — it  leads  to  a  false 
conclusion  :  aluminum  chloride  is  represented  by  the  formula 
A12C16,  hence  the  minimum  molecular  formula  of  indium 
chloride  is  probably  In2Clfi ;  but  this  body  has  been  recently 
gasified  and  shewn  to  have  the  molecular  formula  InCl3. 

The  formula  for  water  was  once  written  HO.  If  potas- 
sium is  thrown  on  to  water,  the  solid  product  of  the  reaction 
is  a  white  salt  whose  formula  may  be  written  HO  .  KO  (O  =  8). 
But  this  substance  is  undecomposed  by  heat,  and  it  exhibits 
none  of  the  reactions  which  a  compound  of  water  with  a 
metallic  oxide  might  be  expected  to  possess,  nevertheless  it 
contains  hydrogen,  oxygen  and  potassium;  when  it  is  fused 
with  potassium,  hydrogen  is  evolved  and  potassium  oxide  re- 
mains. The  oxygen  in  this  substance  cannot  be  removed  in 
parts.  If  the  molecular  formula  of  water  is  written  H2O  (O  =  1 6) 
these  facts  are  explained;  the  white  solid  then  becomes  KHO, 
and  this  formula — as  the  minimum  molecular  formula  of  the 
compound — is  confirmed  by  the  close  analogies  which  exist 
between  the  properties  of  this  body  and  those  of  alcohol, 
the  molecular  formula  of  which  has  been  determined  to  be 
(C2H.)OH.  If  water  is  acted  on  by  chlorine  or  bromine,  the 
simplest  formula  for  the  compound  produced  is  HC1  (or  HBr) ; 


§  36]  ATOMS   AND   MOLECULES.  75 

no  compound  is  formed  with  evolution  of  oxygen  and  con- 
taining oxygen,  hydrogen,  and  chlorine  (or  bromine) ;  this 
formula — HC1 — is  recognised  on  other  grounds  as  the  mole- 
cular formula  of  hydrochloric  acid.  Hence,  it  is  argued,  the 
hydrogen  in  the  molecule  of  water  is  divisible  in  chemical 
changes  into  two  parts,  but  the  oxygen  is  not  divisible,  and 
hence,  the  simplest  molecular  formula  for  water  is  H2O ;  but 
if  this  is  so,  the  atomic  weight  of  oxygen  cannot  be  less 
than  1 6. 

Assuming  the  atomic  weights  of  iron  and  oxygen  to  be 
(in  round  numbers)  56  and  16  respectively,  the  formula  Fe2O3 
is  deduced,  from  analyses,  for  ferric  oxide  as  representing  the 
smallest  quantity  of  this  compound  which  neutralises  acids, 
forms  double  salts,  can  be  acted  on  by  chlorine  to  form 
Fe2Cl6,  &c. ;  hence  this  formula  represents  the  minimum 
molecular  weight  of  ferric  oxide.  But  similar  reasoning 
leads  to  As2O3  as  the  minimum  molecular  formula  of  arse- 
nious  oxide;  now  we  know  that  the  gaseous  oxide  has  a 
molecular  weight  expressed  by  the  formula  As4O6.  Hence  the 
method  of  analogies  does  not  always  lead  to  the  adoption  of 
the  true  molecular  weight  of  a  compound. 

Sometimes  the  method  of  analogies  becomes  very  indirect. 
Thus,  the  molecular  formula  of  ferric  chloride  is  Fe2Cl6,  that  of 
ferrous  chloride  is  either  FeCl2  or  Fe2Cl4.  Ferric  chloride  is 
produced  by  the  action  of  chlorine  on  ferrous  chloride;  now 
the  general  action  of  chlorine  is  either  to  add  itself  on 
to  other  molecules,  or  to  decompose  molecules  and  then 
substitute  itself  for  some  one  or  more  of  the  atoms  formerly 
constituting  these  molecules.  If  ferrous  chloride  is  FeCl2, 
the  action  of  chlorine  on  this  molecule  is  represented  by  the 
equation  2  FeCl2+ C12  =  Fe2Cl6,  but  this  reaction  is  abnor- 
mal. If  ferrous  chloride  is  Fe2Cl4,  the  action  of  chlorine  is 
represented  by  the  equation  Fe2Cl4  + C12  =  Fe2Cl6,  and  this 
reaction  is  analogous  to  other  actions  of  this  element ;  hence 
the  molecular  formula  of  ferrous  chloride  is  probably  not 
smaller  than  Fe2Cl4\ 

1  V.  Meyer  has  recently  obtained  results  regarding  the  vapour  density  of  ferrous 
chloride  which  seem  to  him  to  point  to  the  conclusion  that,  like  stannous  chloride, 


76  CHEMICAL   STATICS.  [§  36 

The  chemical  method  of  determining  minimum  molecular 
weights,  as  applied  to  acids  and  bases,  generally  resolves  itself 
into  determining  the  basicity  of  the  acid,  or  the  acidity  of  the 
base.  Thus,  the  results  of  analyses  of  sulphuric  acid  are 
satisfied  by  the  formula  H2a.SxO4r ;  the  fact  that  this  acid  is 
dibasic  leads  with  a  fair  degree  of  certainty  to  the  con- 
clusion that  x—\y  and  that  the  molecular  formula  of  the 
compound  is  therefore  H2SO4.  The  simplest  formula  which 
can  be  given  to  citric  acid  consistently  with  analytical  results, 
and  with  the  atomic  weights  C  =  12,  O  =  16,  H  =  I,  is  C6H8O7; 
that  the  molecular  formula  is  probably  not  greater  than  this 
is  shewn  by  the  tribasic  character  of  the  acid.  Reasons 
have  been  already  given  for  adopting  NH3  as  the  mole- 
cular formula  of  ammonia :  analysis  shews  that  the  alkaloid 
quinine  cannot  have  a  smaller  molecular  weight  than  that 
represented  by  the  formula  C10H12NO  (C  =  12,  H  =  i,  N  =  14, 
O=  1 6),  but  the  quantity  of  this  alkaloid  which  neutralises 
that  amount  of  hydrochloric  acid  which  is  neutralised  by 
NH3,  is  2C10H12NO,  therefore  the  molecular  formula  of  quinine 
is  probably  not  less  than  C20H24N2O2. 

This  method  may  be  also  applied  to  determine  the  formulae 
of  salts.  Thus  if  sulphuric  acid  has  the  molecular  formula 
H2SO4,  the  molecule  of  sodium  sulphate  is  probably  repre- 
sented by  the  formula  Na2SO4,  because  the  atom  of  sodium 
being  very  probably  monovalent1,  the  amount  of  sodium 
'equivalent'  to  H2  is  represented  by  Na2.  So,  although  boric 
acid  is  non-volatile,  its  ethyl  salt  has  been  vaporised  and 
found  to  have  the  formula  (C2H6)3BO3,  hence,  knowing  that 
boric  acid  is  tribasic,  we  deduce  for  it  the  probable  molecular 
formula  H3BO3. 

The  so-called  'law  of  even  numbers'  enunciated  by  Ger- 
hardt  led  to  the  revision  of  many  molecular  formulae: 
Gerhardt  stated  that  the  sum  of  certain  elementary  atoms 
(hydrogen,  chlorine  and  its  analogues,  nitrogen  and  its  ana- 

this   compound   possesses   two   molecular  weights   expressed  respectively  by  the 
formulae  FeCl2  and  Fe2Cl4;  Ber.  14.  1455. 

1  That  is,  capable  of  combining  directly  with  not  more  than  one  atom  of 
hydrogen,  chlorine,  bromine,  iodine,  or  fluorine  to  form  a  compound  molecule. 
See  chap.  II.,  pars.  56,  57. 


§§  37 '>  3  8]  ATOMS   AND   MOLECULES.  77 

logues)  contained  in  any  molecule  is  always  an  even  number1. 
Thus  analysis  leads  to  the  formula  C2H3O3  for  tartaric  acid, 
and  as  the  acid  is  dibasic  this  formula  is  apparently  mole- 
cular ;  but  the  hydrogen  atoms  must  be  expressed  by  an 
even  number  according  to  Gerhardt's  law,  therefore  the 
formula  was  doubled.  Similar  reasoning  applied  to  the 
formulae  of  nitric  oxide  and  indium  chloride  would  require 
that  these  should  be  written  N.2O2  and  In2Cl6  respectively,  but 
we  know  that  the  molecular  formulae  of  these  compounds  are 
NO  and  InCls,  hence  Gerhardt's  '  law '  must  be  applied  with 
care2. 

37.  The  chemical  methods  for  determining  molecular  and 
atomic  weights  differ  in  two  main  particulars  from  the  phy- 
sical methods  which  have  been  already  discussed. 

The  chemical  methods  as  a  class  do  not  attempt  to 
distinguish  between  solids,  liquids  and  gases — so  far  as  the 
application  of  these  methods  is  concerned  the  molecular 
weight  of  a  solid,  liquid  or  gaseous  substance  is  the  smallest 
quantity  which  takes  part  in  a  chemical  reaction — the  physical 
method  for  finding  molecular  weights  is  only  applicable  in 
any  strictness  to  gases. 

The  chemical  methods  also  generally  begin  by  determin- 
ing, if  possible,  the  atomic  weights  of  the  elements  composing 
a  given  compound,  and  then  argue  as  to  the  molecular  weight 
of  the  compound  ;  the  physical  method,  on  the  other  hand, 
begins  by  defining  molecule,  and  then,  applying  this  definition 
to  chemical  reactions,  arrives  at  a  definition  of  atom,  both 
definitions  being  so  stated  as  to  indicate  the  data  which  are 
required  before  the  relative  weights  of  either  atoms  or 
molecules  can  be  determined. 

38.  In  the  following  table  I  have  sought  to  summarise  a 
•considerable  amount  of  facts  concerning  the  atomic  weights 

of  the  elements  :  it  is  well  that  the  student  should  have  placed 
before  him  a  synopsis  of  the  evidence  on  which  these  all- 
important  numbers  are  based. 

1  See  Laurent,  Chemical  Method,  p.  46  et  seq. 

2  For  further  examples  of  the  application  of  chemical  methods  to  determina- 
tions of  molecular  and  atomic  weights  see  Watts's  Diet.  vol.  I.  pp.  457 — 8  and 
460 — i  ;  also  Williamson  'On  the  Atomic  Theory,'  C.  S.  Journal,  22.  328. 


CHEMICAL   STATICS. 
Atomic   Weights  of  the  Elements. 


[§33 


I 

II 

III 

IV 

Principal  compounds, 

Element 

vapour  densities  of 
•which  have  been 

Specific  heat  : 
how  determined 

Isomorphism  : 
compounds  compared 

determined 

* 

[See  note  A,  p.  84.] 

HYDROGEN 

HF,    HC1,    HBr,    HI, 
H2S,     H2Se,      H2Te, 
H3N,  H3P,  H4C,  &c. 

indirectly  [from  sp.  heat  of  H2O, 
NH4C1,  NH4NO3] 
[atomic  heat  abnormal  ?] 



LITHIUM 

none 

directly 

Li    compounds    with    analogous 

compounds  of  alkali  metals 

BERYLLIUM 

none 

directly  :  not  finally  settled 

a  few  Be  compounds  with  analo- 

-  " 

gous  compounds  of  Cd  and  Zn 

BORON 
CARBON 

BF3,'      BC13V'\  BBr3( 
B(CH3)3     • 
CH4,    CH3F,     CH3C1, 
CH3Br,  CH3T,CHC13, 

directly  :    sp.   heat  varies  much 
with  temperature 
directly:    sp.  heat  varies  much 
with  temperature 

CN  compounds  with  those  of  F, 
Cl,  Br  and  I 

f.." 

CO,C021COCI2,COS, 
CS2,    CHN,    C2H60, 
C4HIOO,  &c. 

NITROGEN 

NH3,  NO,  N0a,  NOC1, 

indirectly  :  very  undecided 

NH4    compounds   with   those  of 

N20,  N204,  &c. 

[from  sp.   ht.    of   various    com- 

alkali metals 

pounds] 

OXYGEN 

OH2,  ON,,  OC,  OC13P, 
02C,  O2S,  03S,  040s, 

indirectly  :  very  undecided 
[from    sp.   ht.    of   various  com- 



&c. 

pounds] 

FLUORINE 
SODIUM 

FH,F(CH3),F3B,F4Si, 
F5P,  &c. 
none 

indirectly  :  very  undecided 
[fromsp.  ht.  ofCaF2,  £c.] 
directly 

metallic  fluorides  with  analogous 
compounds  of  Cl,  Br  and  I 
Na  compounds  with  those  of  other 

alkali  metals 

MAGNESIUM 

none 

directly 

Mg    compounds    generally    with 

those  of  Zn,  Mn,  and  Fe  (in  fer- 

rous salts) 

ALUMINIUM 

A12C16J  Al2Br6,  A1aI6 

directly 

with  Cr,  Mn  and  Fe  in  R2O3  and 

derivatives 

SILICON 

SiF4,        SiCl4,        SiI4, 

Si(CH3)4,                     SlHgCl, 

Si.3OCl6,   Si20(C2H5)6 

directly  :    sp.    ht.    varies  much 
with  temperature 

with  C,   Zr,  Sn  and  Ti  in  com- 
pounds of  type  RO2 

PHOSPHORUS 

PH3,   PC13,    PIa,    PF5, 

POClg,       PSCI3,        PoI4, 

directly 

phosphates  with    vanadates  and 
arsenates,    organic    compounds 

P2H4,  P3N3C16,  &c." 

of  P  with  those  of  N,  As  and  Sb 

SULPHUR 

SH2,  S00,  S03,  SOC12, 

directly 

with    Se    compounds,    with     Te 

SaC,  S2C12,  &c. 

compounds  of  type  R"Te.    Salts 

of  H2SO4  with  those  of  H2SeO4 

and  H2Te04 

CHLORINE 

C1H,     C1(CH3),     C1T1, 
Cl2Zn,  Cl2Hg,  C13HC, 
Cl,Bi,     Cl3Sb,     C14C, 

indirectly  :  doubtful 
[from  comparison  of  specificheats 
of  various  haloid  compounds] 

Chlorides,   with  analogous  com- 
pounds of  Br  and  I 

Cl4Si,     Cl4Ti,     Cl.Ta, 

ClsMo,  C1,W,  &c. 

POTASSIUM 

none 

directly 

K  compounds  with  those  of  other 

alkali  metals 

CALCIUM 

none 

directly 

Ca  compounds  with  those  of  Sr, 

Ba,  and  in  some  cases  Pb 

SCANDIUM 

none 

sp.  heats  of  some  compounds  de- 

[? Sc   compounds  with   those   of 

termined 

other  earth  metals] 

TITANIUM 

TiCl4 

sp.   heats  of  a  few  compounds 

TiO2  and  some  derivatives  with 

determined 

analogous  compounds  of  C,  Si, 

Zr,  Sn  and  Th 

VANADIUM 

vcu,  voci3 

sp.   heats  of  one   or  two    com- 

Vanadates with   phosphates  and 

pounds  determined 

arsenates 

38] 


ATOMS   AND   MOLECULES. 

Atomic  Weights  of  the  Elements. 


79 


V 

VI 

VII 

VIII 

Atomic  %veight 

(i) 

by  vapour 
density 
method 

(2) 

by  sp,  heat 
method 

Compounds  analysed,  &c. 
in  order  to  find  combining 
weight  of  the  element 

Combining 
weight 

Remarks 

[for  more  details  concern- 
ing these  numbers  see 
Tables,  pp.  37  —  40  and 
pp.  48—  49.] 

[See  note  B,  p.  84.] 

[See  note  C,  p.  84.] 

-  

7-01 

i  Lithium  chloride 

7-01 



9-08 

2  Beryllium  sulphate 

4'54 

^«2522fe*^ 

10-95 

«>'95 

3  Borax,  boron  chloride 

3-65 

^^**^    T  -^•^^''w 

Xjf^-L-ej^sw 

11-97 

11-97 

4  Diamond  burnt  to  COa 

2-99 

14*01 



8  Ammonium    chloride,      silver 
nitrate 

4*67 

'    ^^$ft  "WT  k   ' 

.5,6 



6  Synthesis  of  water 

r* 

^^~^WlJXv 

19*1 

— 

23 

"  Sodium    fluoride,      potassium 
fluoride,  calcium  fluoride 
8  Sodium  chloride 

19-1 
23 

27'O2 

[see  p.  56] 
28 

24 

27*02 
28 

9  Magnesium      sulphate,       do. 
chloride,   synthesis   of   mag- 
•    nesium  sulphate 
10  Ammonia    alum,      aluminium 
bromide,   solution  of  alumin- 
ium in  soda 
11  Silicon  chloride 

12 

9  '007 
7 

30-96 

30-96 

12  Phosphorus  chloride,  synthesis 
of  phosphorus  pentoxide 

10*32 

3i  '93 

31  '98 

13  Synthesis   of    silver   sulphide, 
reduction   of  silver  sulphate 
by  hydrogen 

10*66 

35'37 



14  Potassium   chlorate,  synthesis 
of  silver  chloride 

35'37 

48 

SI'2 

39'°4 
39  '9 

15  Potassium  chloride,    do.    bro- 
mide 
16  Calcium  chloride,  calcium  car- 
bonate 
17  Synthesis    of    scandium    sul- 
phate 
18  Titanium     chloride,     bromide 
and  oxide 

19  Vanadium  pentoxide,  do.  oxy- 
chloride 

39'04 
14-68 

12 

I2'8 

Sc.     The  atomic  weight  of  this  metal 
is  most  probably  14-68  X  3  =  44*04  :  if 
this  is  so,  the  oxide  is  written  Sc2O3 
and  is  thus  shewn  to  be  analogous 
with  the  oxides  of  the  earth  metals. 

8o 


CHEMICAL  STATICS. 
Atomic  Weights  of  the  Elements. 


[§33 


< 

II 

III 

IV 

Element 

Principal  compounds, 
vapour  densities  of 
which  have  been 

Specific  heat  : 
how  determined 

Isomorphism  : 
compounds  compared 

determined 

[See  note  A,  p.  84.] 

CHROMIUM 

CrO2Cla 

directly  [?  too  low] 

Salts   of  H2CrO4  with   those  of 

H2MnO4   and   H,TeO4,    Cr2O- 
with  AUO3,  Mn2O3  and  Fe2U3  * 

MANGANESE 

none 

directly  [?  too  high] 

Mn2O3    with   A12O3,    Cr2O3   and 
Fe2O3,    R2MnO4  with   R2CrO< 

and      R2TeO4,     RMnO4    with 
RC104 

IRON 

Fe2Cl8 

directly 

Fe2O3  and  derivatives  with  A1203, 
Cr2O3.  Mn2O3  and   derivatives 
some  Fe  salts  with  those  of  Ni, 

Co,  and  Cu 

NICKEL 

none 

directly 

Ni  with  Co  compounds,  some  Ni 
compounds  with    those    of   Fe 

(ferrous  salts) 

COBALT 

none 

directly 

Co  with  Ni  compounds,  some  Cc 

compounds   with    those    of   Fe 

(ferrous  salts) 

COPPER 

Cu2Cl2 

directly 

most  Cu  compounds  with  those  oi 

Ni  and  Co,  some  with  Fe  (fer- 

rous) compounds,   Cu  with  Ag 

ZINC 

ZnCl2)        Zn(CH3)2, 

directly 

compounds  of  type  R2O 
Zn  compounds  with  those  of  Mg 

Zn(C2H,)2 

and  Mn 

GALLIUM 

Ga2Cl6 

directly  [?  too  low] 

Ga  alum  with  other  alums 

ARSENIC 

AsH3,      AsCl3,      AsI8, 
As(CH3)2Cl,       As406, 

directly 

As  compounds  with  those  of  Sb 
and   Bi,  organic   compounds  ol 

&c. 

As  with  those  of  N,  P,  and  Sb. 

arsenates  with   phosphates  and 

vanadates 

SELENION 

SeH2,  Se02 

directly 

Se  with  S  compounds 

BROMINE 

BrH,    Br(CH3),  Br2Cd, 
Br3B,  Br4Sn,  Br4U,  &c. 

directly 

Bromides    with    analogous   com- 
pounds of  Cl  and  I 

RUBIDIUM 

none 

indirectly  :  doubtful 
[from  comparison  of  specific  heats 

Rb  compounds  with  those  of  othei 
alkali  metals 

of  some  compounds  with  those 

of  other  alkali  metals] 

STRONTIUM 

none 

indirectly  :  doubtful 
[comparison  of  specific  heats  of 
compounds  of  Sr,  Ca,  and  Ba] 

Sr  compounds  with  those  of  Ca 
and  Ba,  and  with  some  Pb  salts 

YTTRIUM 

none 

sp.  heats  of  a  few  compounds  de- 
termined 

Yt  compounds  with  those  of  othei 
earth  metals 

ZIRCONIUM 

ZrCl4 

directly  [?  too  low] 

ZrOo  with  TiO2,  ThO,,  SnO2  and 

NIOBIUM 

NbCl3,  NbOCl, 

^___ 

Si62 
Nb  with  Ta  compounds,  Nb  flu- 

orides and  oxyfluorides  with  Me 

MOLYBDENUM 

MoCla 

directly  [?  too  high] 

do.  do. 
Mo   with    W    compounds,    som< 

salts  of  H2MoO4  with  those  o: 

H2CrO4,  Mo  with  Nb  fluoride' 

and  oxyfluorides 

§38] 


ATOMS  AND   MOLECULES. 
Atomic  Weights  of  the  Elements. 


Si 


V 

VI 

VII 

VIII 

Atomic  weight 

(*) 

(2) 

y  vapoitr 
density 
method 

by  sp.  heat 
method 

Compounds  analysed,  &>c. 
in  order  to  find  combining 
weight  of  the  element 

Combining 
weight 

Remarks 

)r  more  details  concern- 

ng  these  numbers  see 
Tables,  pp.  37  —  40  and 

[See  note  B,  p.  84.] 

[See  note  C,  p.  84.] 

pp.  48—  49.] 

52  '4 

52-4 

20  Chromium      chloride,      silver 

26-2 

chromate,  potassium  dichro- 

mate 



55 

21  Manganese  chloride,  mangan- 

27-5 

ous-manganic     oxide,     man- 

ganous    oxalate,    silver  per- 

manganate, &c. 

55-9 

55  '9 

22  Synthesis     of     ferric     oxide, 

27'95 

see  p.  56] 

reduction    of    ferric     oxide, 

analysis  of  ferrous  and  ferric 

chlorides 



58-6 

23  Nickel  chloride,  nickelous  ox- 

29*3 

ide,  strychnine-nickel  cyanide, 
brucine-nickel  cyanide,  &c. 



59 

24  Ammonium  -  cobalt      cyanide, 

29'5 

phenyl-ammonium  cobalt  cy- 

anide,   strychnine    and    bru- 

cine-cobalt  cyanides 

63'4 

63H 

25  Reduction    of   copper    oxide, 

31  '7 

ee  p.  56] 

electrolysis    of    copper    sul- 

phate, &c. 

64-9 

64-9 

26  Synthesis  of  zinc  oxide,  analy- 

32 "3 

69 

69 

sis  of  potassium-  zinc  chloride 
27  Oxidation  of  the  metal,  analy- 

23 

. 

ee  p.  56] 

sis  of  gallium-ammonia  alum 

74'9 

74  '9 

28  Arsenic  bromide,  do.  chloride, 

24-97 

do.  oxide 

78-8 

78-8 

29  Reduction  of  selenion  dioxide, 

39  "4 

reduction  of  silver  selenite 

79V5 

79'75 

30  Synthesis  of    silver  bromide, 

79'75 





analysis  of  potassium  bromide 
31  Rubidium  chloride 

85-2 

Rb.    From  analogies  between  Rb  (and 

its  salts)  and  the  metals  of  the  al- 

kalis, the  formulae  RbCl,  Rb2O,  &c. 

are  most  probably  correct  :  if  so,  the 
atomic  weight  of  Rb  is  to  be  taken 

as  equal  to  its  combining  weight. 





32  Strontium  chloride 

43-65 

Sr.     The  atomic  weight  of  strontium 

must  be  taken  as  4:5*65  X  2  =  87-3  if 
the  formulae   of  its  salts  are  to  be- 

come analogous  to  those  of  the  Ba 

90 

90 

33  Synthesis  of  yttrium  sulphate 

34  Zirconium  chloride,  potassium- 
zirconium  fluoride 

29-87 
45 

and  Ca  salts. 
Yt.     Atomic  weight  probably  =  29*87 
X  3  =  89-6  because  of  analogy  of  Yt 
salts  with  those  of  earth  metals. 

94 

__ 

35  Niobium  chloride,  potassium- 

. 

niobium  oxyfluoride 

95-8 

95'8 

36  Molybdenum  dichloride,  tetra- 

19*16 

chloride  and  pentachloride 

M.  C. 

6 

82 


CHEMICAL   STATICS. 
Atomic  Weights  of  the  Elements. 


I 

II 

III 

IV 

Element 

Principal  compounds, 
vapour  densities  of 
"which  havs  been 

Specific  heat  : 
how  determined 

Isomorphism  : 
compounds  compared 

determined 

[See  note  A,  p.  84.] 

RHODIUM 

none 

directly 

most  Rh  compounds  with  thos 
Ru,  Pd,  Ir,  Pt  and  Os 

RUTHENIUM 

none 

directly 

most  Ru  compounds  with  thos< 
Rh,  Pd,  Ir,  Pt  and  Os 

PALLADIUM 

none 

directly 

most  Pd  compounds  with  thos< 

Ru,  Rh,  Ir,  Pt  and  Os 

SILVER 

none 

directly 

some  Ag  compounds  with  thos 
Na  and  other  alkali  metals, 

with    Cu    compounds    of    t 

R2O,   a  few  Ag  and  Au   ci 

pounds 

CADMIUM 

CdBr2 

directly 

some  Cd  compounds  with  thos 

Be  and  Zn 

INDIUM 

InCl3 

directly 

some  In  compounds  with  thos' 

Cd  and  Be 

TIN 

SnCl2,  SnCl4,  Sn2Cl4 

directly 

SnO2  with  TiO2)  ZrO2  and  Th 

ANTIMONY 

ShHs,      SbCl3,      SbF3, 

directly 

Sb  compounds  with  those  of 

Sb(CH3)3 

andBi 

IODINE 

IH,  IC1,  I(CH3^,  I2P4, 
I2Hg,  ISP,  I3As,  I4Si, 

directly 

Iodides     with    analogous     c 
pounds  of  Cl  and  Br 

TELLURIUM 

I6A12,  &c. 
Tell, 

directly 

most  Te  compounds  with  tl 

of  Sand  Se 

CAESIUM 

none 

indirectly  :  doubtful 

Cs  compounds  with  those  of  o 

[comparison  of  specific  heats  of 

metals  of  alkalis 

compounds  with  those  of  other 
alkali  metals] 

BARIUM 

none 

indirectly  :  doubtful 

Ba  compounds  with  those  of 

[comparison  of  specific  heats  of 
compounds  of  Ca,  Sr,  and  Ba] 

and  Sr 

LANTHANUM 

none 

directly 

CERIUM 

none 

directly 

most  La  compounds  with  tho; 

DIDYMIUM 

none 

directly                                         j> 

Ce,  Di,  Er  and  Yt,  some  c 
pounds  of  these  metals  with 

ERBIUM 

none 

sp.  heats  of  a  few  compounds 

compounds 

determined 

YTTERBIUM 

none 

sp.   heats  of  a  few  compounds 
determined 

[?  a  few  Yb  compounds  with  t 
of  other  earth  metals] 

TANTALUM 

TaCl5 

Ta  with  Nb  compounds 

TUNGSTEN 

WOC14,  WC15,  WC16 

directly 

W  with   Mo    compounds,   s 
salts  of  H2W04  with  thos 
H2Cr04  and  H2TeO4 

IRIDIUM 

none 

directly                                            \ 

OSMIUM 

OsO4 

directly 

Os,   Ir  and  Pt  compounds 
those  of  Ru,  Rh  and  Pd 

PLATINUM 

none 

directly                                          ) 

38] 


ATOMS   AND   MOLECULES. 
Atomic  IV eights  of  the  Elements. 


V 

VI 

VII 

VIII 

Atomic  weight 

~~  (i)                (2) 

y  vapour 
density 
method 

by  sp.  heat 
method 

Compotmds  analysed,  6°<r. 
in  order  to  find  combining 
weight  of  the  element 

Combining 
weight 

Remarks 

:>r  more  details  concern- 

ing these  numbers  see 
Tables,  pp.  37—40  and 

[See  note  B,  p.  84.] 

[See  note  C,  p.  84.] 

pp.  48—49-] 



104 

37  Potassium-rhodium  chloride 

26 

(103 

37a  Purpureo-rhodiumchloro-and 

(25-75) 

bromo-compounds) 



104*5 

38  Potassium-  ruthenium  chloride 

26-1 



106*2 

39  Palladium  chloride 

26-55 



107-66 

40  Silver  chlorate,bromate,iodate, 

107*66 

synthesis    of   silver   bromide 

and  iodide 

112 

112 

41  Cadmium  bromide 

56 

"3"4 

1  13  '4 

42  Synthesis  of  indium  oxide 

37-8 

117-8 

117-8 

43  Synthesis  of  stannic  oxide 

58-9 

1  20 

1  20 

44  Antimony  bromide,  reduction 

40 

of  antimony  oxide,  also  analy- 
sis of  antimony  sulphide 

126-53 

126-53 

45  Silver    iodate,    silver    iodide, 

126-53 

synthesis  of  do. 

)  127-5 

(?)  127-5 

46  Oxidation  of  tellurium,  analy- 
sis   of    potassium  -  tellurium 

63-75 

Te.    Very  possibly  the  atomic  weight 
of  Te   is  less  than  that  of  iodine. 

bromide 

[See  note  on  p.  87.] 





47  Caesium  chloride 

132-7 

Cs.  This  metal  certainly  belongs  to  the 
alkali  metals—  hence  the  chloride  is 

CsCl,  and,  if  so,  the  atomic  wt.  =132*7. 





48  Barium  chloride 

68-43 

Ba.     Atomic  weight  probably  68-43 

X  2  =  136-86  because  of  analogies  be- 

tween salts  of  Ba,  Sr  and  Ca. 



138-5 

49  Lanthanum  sulphate,  do.  ox- 

46-17 

ide,  do.  oxalate 



141 

50  Cerium  oxalate 

47 



144 

51  Didymium  oxide  and  sulphate 

48 

(142 

5la 

47-6) 



53  Erbium  sulphate 

55'33 

Er.    This  metal  belongs  to  the  earth 
group,  hence  the  atomic  weight  is 

— 

— 

•&  Ytterbium  sulphate 

57  '69 

taken  as  55*33  X  3  =  166. 
Yb.     For    similar   reasons    to    those 
which  apply  in  cases  of  Sc,  Yt  and 

182 



54  Potassium  -  tantalum    fluoride, 

60-67 

Er,  the  atomic  weight  of  Ytterbium 

183-6 

183-6 

ammonium-  tantalum  fluoride 
55  Reduction    of  tungstic   oxide, 

30  '6 

is  supposed  to  be  3  times  its  combin- 
ing weight  (=  173). 

analysis  of  tungsten  hexclor- 
ide 

•  

192-5 

56  Potassium-iridium  chloride 

48.13 

T93 

193 

57  Osmium  tetroxide 

48-25 

Os.    The  number  given  is  calculated 

from    2    determinations    of   vapour 

~ 

194-3 

58  Potassium-platinum  chloride 

48-575 

density    of   OsO4    by  Deville  and 
Debray,    other   experimenters  have 
found  numbers  for  atomic  weight  of 

this  metal  varying  from  195  to  199. 

6—2 


84 


CHEMICAL   STATICS. 
Atomic  Weights  of  the  Elements. 


[§33 


I 

II 

III 

IV 

Element 

Principal  compounds  ^ 
vapour  densities  of 
which  have  been 

Specific  heat  ; 
hcnv  determined 

Isomorphism  : 
compounds  compared 

determined 

[See  note  A,  p.  84.] 

GOLD 

none 

directly 

some  Au  compounds  with  thos< 
Ag,  a  few  Au  compounds  w 

those  of  Ni  and  Fe 

MERCURY 

[HgCI]    HgCI*    HgI2) 

directly 

Hg  and  Cu  compounds  of  13 
RO 

THALLIUM 

Tic! 

directly 

Tl   compounds  with  those  of 

of  type  RC13,  Tl  compounds 

type  T1C1  with   those  of  all 

metals 

LEAD 

PbCL,,  PKCH3)4 

directly 

some  Pb  with  Tl  compounds,  m? 

Pb  with  Cu  and  Hg  compom 

BISMUTH 

BiCl3,   BiF3)  Bi(CH3)3, 

directly 

Bi  compounds  with  those  of 

&c. 

and  Sb 

THORIUM 

none 

directly 

ThOo  with  SiO2)  Ti02)  Sn02  z 
ZrO"2 

URANIUM 

UC14,  UBr4 

directly 

some   compounds  of  type   U> 

with  those  of  Al,  Cr,  Mn  and 

Notes  to  Table  of  Atomic  Weights. 

A.  As  the  method  based  on  isomorphism  of  compounds  is  chiefly  used  as  a 
means  of  verifying  values  assigned  to  atomic  weights  by  other  methods,  no  num- 
bers are  given  in  column  IV.,  but  merely  an  indication  of  the  various  compounds 
which  have  been  compared  crystallographically,  and  on  which,  arguments  for  or 
against  a  given  value  for  the  atomic  weights  in  column  v.  have  been,  or  may 
be,  based. 

B.  This  column  (vi.)  is  not  to  be  regarded  as  containing  anything  like  a 
complete   summary  of  the  processes   employed  for   determining  the   combining 
numbers  of  the  elements ;  only  the  more  important  processes  are   indicated  ; — 
references  are  given  to  the  original  papers. 

A  complete  account  of  all  researches  on  this  subject  will  be  found  in  A  Re- 
calculation of  the  Atomic  Weights,  by  F.  W.  Clarke  [Part  v.  of  the  Constants  of 
Nature  published  by  the  Smithsonian  Institution],  and  also  in  Die  Atomgewichte 
der  Elemente,  by  L.  Meyer  and  K.  Seubert  [Leipzig,  1883]. 

C.  When  the  atomic  weight  given  in  column  v.  section  (2)  is  a  multiple  of 
the  combining  number  in  column  vn.,  no  number  being  given  in  section  (x)  of 
column  v.,  it  is  to  be  inferred  that,  besides  the  argument  drawn  from  the  value 
of  the  specific  heat  of  the  element  in  question,  there  are  other  chemical  reasons 
for  adopting  the  special  multiple  which  appears  in  v.  (2) :  these  reasons  may  be 
broadly  described  as  based  on  analogies  between  salts  of  the  given  element  and 
salts  of  other  elements,  the  atomic  weights  of  which  have  been  established  by  the 
two  leading  physical  methods. 


ATOMS   AND   MOLECULES. 
Atomic  Weights  of  the  Elements. 


V 

Atomic  weight 

VI 

VII 

VIII 

'>y  vapour 
density 
metJiod 

(2) 

by  sp.  JiccU 
method 

Compounds  analysed,  &"c. 
in  order  to  find  combining 
%veight  oj  the  element 

Combining 
weight 

Remarks 

or  more  details  concern- 
ing these  numbers  see 
Tables,  pp.  37  —  40  and 
pp.  43—49-] 

[See  note  B,  p.  84  ] 

[See  note  C,  p.  84.] 



*  

196 

59  Gold  chloride,  potassium-gold 
chloride 

65-33 

IQQ'8 

199-8 

60  Mercuric  chloride,  do.  oxide 

99  '9 

303  64 

203-64 

61  Synthesis  of  thallium  nitrate 

203-64 

206  '4 
208 

208 
232  '4 

62  Synthesis  of  lead  nitrate,  do, 
do.  sulphate 
63  Synthesis  of  bismuthous  oxide, 
&c.,  analysis  of  bismuthous 
chloride 
64  Thorium  sulphate 

103-2 

58-r 

240 

240 

65  Uranium  acetate,  do.  oxalate 

60 

References  to  Table  of  Atomic  Weights. 

1  Li.     J.  W.  MALLET,  Sill.  Amer.  Journal  (2)  22.  349.      STAS,   Nonvclles 
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3  B.     BERZELIUS,  Pogg.  Ann.  2.  129.     DEVILLE,  Ann.  Chim.  Phys.  (3)  55. 
1 80. 

4  C.     DUMAS    and    STAS,   Ann.    Chim.   Phys.    (3)   1.   5.      ERDMANN    and 
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5  N.     STAS,  Rapports,  pp.  50,  87,  92  ;  and  Nouvdles  Recherches,  pp.  57,  281. 

6  O.     ERDMANN  and  MARCHAND,  J.  fiir  pract.  Chemie,  26.  468.     DUMAS, 
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10  Al.     J.  W.  MALLET,  Phil.  Trans,  for  1880.  1003  et  seq, 

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86  CHEMICAL   STATICS.  [§38 

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15  K.     STAS,  Rapports,  pp.  69,  91,  118;  and  Nouvelles  Recherches,  p.  244. 

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§  38]  ATOMS  AND   MOLECULES.  8/ 

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12.   222. 

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55  W.     ROSCOE,  Chem.  Neivs,  25.  61,  73. 

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59  ^4«.     BERZELIUS,  Lehrbuch,  (sth  ed.)  3.  1212.    JAVAL,  Ann.  Chim.  Phys. 
17.  337.     LEVOL,  Ann.  Chim.  Phys.  (3)  30.  355. 

60  Hg.     ERDMANN  and  MARCHAND,  J.  fur  pract.  Chemie,  31.  392.     SVAN- 
BERG,  J.furpract.  Chemie,  45.  468.     MILLON,  Ann.  Chim.  Phys.  (3)  18.  345. 

61  77.     W.  CROOKES,  Phil.  Trans,  for  1873.  277. 

62  Pb.     STAS,  Rapports,  pp.  101  and  106. 

63  Bi.     SCHNEIDER,  Pogg.  Ann.  82.  303.     DUMAS,  Ann.  Chim.  Phys.  (3)  55. 
176.    MARIGNAC,  Archiv.  Scien.  Phys.  nat.    (3)  10.  5,  193.      LOWE,  Zeitschr. 
anal.  Chemie,  22.  498. 

64  Th.     NILSON,  Ber.  15.  2527. 

65  U.     PELIGOT,  Ann.  Chim.  Phys.  (3)  20.  329. 

Note.  The  full  titles  of  Stas's  treatises  which  are  referred  to  in  this  table 
are :  (i)  Recherches  sur  les  rapports  reciproqties  des poids  atomiques,  par  J.  S.  Stas, 
Bruxelles,  1860.  (2)  •Nouvelles  recherches  sur  les  lois  des  proportions  chimiques, 
sur  les  poids  atomiques  et  leur  rapports  mutuels,  par  J.  S.  Stas,  Bruxelles,  1865. 
A  translation  into  German  of  both  treatises  was  published  in  1867  under  the  title 
Untersuchungen  iiber  die  Gesetze  der  Chemischen  Proportionen,  iiber  die  Atomge- 
wichte  und  ihre  gegenseitigen  Verhdltnisse. 

1  BRAUNER  (see  abstract  in  Ber.  16.  3055)  has  recently  obtained  values  for  the  atomic  weight 
of  Tellurium  varying  from  124*94  to  I25'4  (mean  =  125)  ;  he  has  shewn  that  the  process  employed 
by  Wills  gives  values  which  are  too  high,  unless  great  precautions  are  taken. 


39 


CHAPTER    II. 


ATOMIC   AND   MOLECULAR   SYSTEMS. 


SECTION  I.     Nascent  Actions. 

39.  BRODIE  applied  his  hypothesis  regarding  the  structure 
of  elementary  molecules  (see  ante,  p.  71,  par.  36)  to  explain  a 
number  of  phenomena  generally  grouped  together  under  the 
name  nascent  actions.  That  explanation,  somewhat  simplified 
and  also  developed  by  subsequent  research,  is  usually  regarded 
as  the  most  satisfactory  that  can  be  given  in  the  present  state 
of  knowledge. 

When  hydrogen  is  passed  into  water  containing  silver 
chloride  in  suspension  no  chemical  change  occurs ;  when 
hydrogen  is  generated  in  the  vessel  which  contains  the  silver 
chloride  decomposition  of  this  salt  proceeds  rapidly  with  pro- 
duction of  silver  and  hydrochloric  acid.  Nitrobenzene  is  con- 
verted into  aniline  by  the  action  of  hydrogen  produced  in 
contact  with  it,  but  not  by  hydrogen  produced  in  another 
vessel  and  conducted  into  that  containing  the  nitrobenzene. 
Carbon,  hydrogen,  and  nitrogen  do  not  combine  directly; 
but  if  electric  sparks  are  passed  through  a  mixture  of  benzene 
vapour  and  nitrogen,  hydrocyanic  acid  is  produced.  Sulphur 
dioxide  and  water  when  heated  with  oxygen  are  only  very 
partially  changed  into  sulphuric  acid ;  but  if  the  oxygen  is 
produced  in  contact  with  the  moist  dioxide  (e.g.  by  decompo- 
sition of  nitrogen  trioxide)  the  change  into  sulphuric  acid  is 


§  40]  ATOMIC   AND   MOLECULAR   SYSTEMS.  89 

rapidly  completed.  Sulphur  is  not  oxidised  to  sulphuric  acid 
by  bromine  in  presence  of  water ;  but  if  the  sulphur  is  pro- 
duced from  a  compound  in  presence  of  bromine  water,  it  is 
then  oxidised  (e.g.  sulphuretted  hydrogen  passed  into  bromine 
water  gives  hydrobromic  acid  and  sulphur,  and  also  sul- 
phuric acid).  Metallic  chlorides  (e.g.  aluminium  chloride) 
produced  by  the  action  of  metal  on  chlorine  only  at  very 
high  temperatures,  and  in  small  quantities  for  a  given  time 
of  action,  are  sometimes  much  more  easily  prepared  by  the 
action  of  chlorine  on  a  mixture  of  the  metallic  oxide  and 
carbon.  The  general  action  of  metals  on  dilute  cold  sulphuric 
acid  is  to  produce  a  sulphate  and  evolve  hydrogen,  but  on 
nitric  acid  to  produce  a  nitrate  and  evolve  oxides  of  nitrogen, 
nitrogen  and  ammonia ;  many  metals  when  heated  with  con- 
centrated sulphuric  acid  evolve  sulphur  dioxide,  either  alone, 
or  in  some  cases  mixed  with  hydrogen  and  sulphuretted 
hydrogen. 

40.  These  phenomena,  and  many  others  of  the  same 
class,  find  an  explanation  in  terms  of  the  molecular  theory, 
that  explanation  being  based  on  the  distinction,  already 
insisted  on,  between  molecules  and  atoms.  Any  mass  of  a 
gaseous  element  under  ordinary  conditions  is  built  up  of 
molecules,  but  if  we  assume  that  when  a  compound  molecule 
undergoes  decomposition  a  short  but  appreciable  time  elapses 
before  the  greater  number  of  the  elementary  atoms  which 
composed  it  have  rearranged  themselves  to  form  new  mole- 
cules, we  have  the  materials  for  a  fairly  satisfactory  explana- 
tion of  the  phenomena  of  nascent  action.  This  explanation 
does  not  necessitate,  as  some  of  its  French  opponents  say  it 
does,  the  assumption  of  strange  and  inexplicable  properties  as 
belonging  to  the  elementary  atoms.  Indeed  the  existence  of 
what  is  known  as  the  ' nascent  state'  seems  to  follow  as  a 
necessary  deduction  from  the  molecular  theory  applied  to 
chemical  phenomena.  When  a  chemical  change  occurs 
between  two  molecules,  the  first  step  in  that  change  must  in 
most  cases  consist  in  a  breaking  up  of  the  molecular  struc- 
tures, and  the  second,  in  a  rearrangement  of  the  parts  of  the 
molecules,  i.e.  of  the  atoms,  to  form  a  configuration  stable 


90  CHEMICAL  STATICS.  [§  41 

under  the  conditions  of  the  experiment:  if,  by  the  presenta- 
tion of  molecules  of  a  third  chemical  substance,  there  is  ren- 
dered possible  the  adoption  by  the  various  atoms  of  another 
configuration,  more  stable  than  that  just  supposed  to  be 
assumed,  this,  the  most  stable  configuration,  will  be  adopted. 
But  if  the  earlier  stable  configuration  has  been  assumed  by 
the  atoms,  it  does  not  follow  that  the  introduction  of  the 
third  class  of  molecules  will  now  cause  this  configuration  to 
become  unstable1. 

41.  Following  out  this  line  of  argument,  it  would  appear 
probable  that  compounds  should  present  phenomena  some- 
what analogous  to  those  exhibited  by  elements  when  in  the 
nascent,  i.e.  on  the  hypothesis  now  adopted,  atomic  state. 
Let  it  be  supposed  that  no  chemical  change  occurred 
when  the  compound  molecules  a  and  b  were  brought  into 
contact,  nevertheless  if  the  atoms  constituting  these  molecules 
were  allowed  to  react  a  chemical  change  might  occur.  In  a 
reaction  wherein  the  given  compound  is  produced  there  must 
be  a  moment  of  time  when  this  compound  can  only  be  said 
to  exist  potentially,  when  the  atoms  which  constitute  its 
molecules  have  not  settled  down  into  stable  configurations ; 
at  this  moment  the  compound  may  be  said  to  exist  in  the 
nascent  state.  If  the  atomic  vibrations  and  interactions  are 
allowed  to  run  what  may  be  called  their  normal  course,  the 
compound  molecules  are  certainly  produced,  but  if  these 
interactions  are  interfered  with,  a  new  set  of  molecules  may  be 

1  It  may  be  urged  that  the  energy  (or  part  of  the  energy)  which  is  used  in 
decomposing  the  molecules  of  the  reacting  substances  is  gained  by  the  atoms 
thence  produced,  and  that  the  only  difference  between  e.g.  ordinary  and 
'nascent'  hydrogen,  is  to  be  found  in  the  greater  chemical  energy  of  the  latter. 
The  importance  of  this  point  of  view  is  of  course  admitted  by  the  upholders  of 
the  atomic  explanation  of  nascent  actions,  but  they  would  supplement  this  by  the 
statement  that  the  configuration  with  which  the  greater  quantity  of  energy  is 
associated  is  atomic,  and  they  contrast  this  with  a  molecular  and  comparatively 
inactive  configuration. 

The  experiments  of  Victor  Meyer  on  iodine  give  direct  evidence  of  the 
separation  of  elementary  molecules  into  atoms  by  the  addition  of  energy  in  the 
form  of  heat.  (See  ante,  p.  31  par.  15.) 

In  book  II.  chapter  n.  will  be  found  some  facts  regarding  dissociation  which 
bear  on  the  subject  of  nascent  actions. 


§41]  ATOMIC   AND   MOLECULAR   SYSTEMS.  QI 

formed,  which  molecules  bear  a  more  or  less  simple  genetic 
relation  to  those  produced  in  the  normal  process  of  chemical 
change1. 

The  following  among  other  cases  of  chemical  change  find 
a  partial  explanation  in  terms  of  this  hypothesis.  Nitrous 
acid  has  no  action  on  the  primary  mononitroparaffins 
(CnH27z+1 .  NOJ,  but  these  compounds  are  converted  into 
nitrolic  acids  (CnH2n .  N2O3)  by  the  action  of  potassium 
nitrite  and  sulphuric  acid,  i.e.  by  the  action  of  potentially 
formed  nitrous  acid.  Nitric  acid  does  not  act  on  napthol  to 
produce  dinitronapthol,  but  if  napthol  be  produced  in 
contact  with  nitric  acid — e.g.  by  boiling  diazonapthalene 
hydrochloride  in  presence  of  nitric  acid — dinitronapthol  is 
formed.  Carbon  monoxide  and  ethylene  do  not  react  to  form 
acrolein  even  under  the  influence  of  electric  sparks,  but  if 
ethylene  is  exploded  with  a  quantity  of  oxygen  less  than 
sufficient  for  complete  oxidation,  carbon  monoxide  is  pro- 
duced and  simultaneously  acrolein  is  formed,  i.e.  the  chemical 
change  proceeds  partly  in  its  normal  way  and  at  the  same 
time  the  atoms  of  the  'nascent'  carbon  oxide  react  on  the 
ethylene  molecules  with  production  of  acrolein.  When 
pariodophenol  is  fused  with  potash  at  163°  hydroquinone 
is  produced,  but  at  higher  temperatures  only  resorcin  is 
formed :  now  as  fusing  potash  does  not  act  on  hydroquinone 
it  seems  necessary  to  conclude,  that  in  the  fusion  of  pariodo- 
phenol at  high  temperatures  hydroquinone  is  produced, 
but  is  immediately  changed  into  resorcin.  Many  olefines 
(e.g.  amylene)  are  polymerised  by  the  action  of  sulphuric 
acid  :  the  most  probable  explanation  of  this  action  assumes 
that  an  unstable  compound  of  olefine  and  sulphuric  acid 
is  produced  and  again  decomposed,  and  that  the  molecules 

1  In  all  such  considerations  we  can  deal  with  molecular  phenomena  only  by  a 
statistical  method,  we  can  reason  only  as  to  the  average  condition  of  the  mass  of 
molecules  constituting  a  substance  at  any  moment  of  time. 

It  seems  not  improbable  that  there  may  sometimes  be  as  great  differences 
between  the  properties  of  a  number  of  elementary  atoms  all  of  one  kind  and  the 
elementary  molecules  which  are  produced  by  the  union  of  these  atoms,  as  between 
the  properties  of  a  number  of  atoms  of  different  kinds  and  the  compound  mole- 
cules produced  by  the  union  of  these  atoms. 


92  CHEMICAL   STATICS.  [§§  41  42 

of  olefine  as  they  are  set  free  from  this  compound  coalesce 
to  form  polymeric  molecules.  By  carrying  the  explanation 
a  little  further,  and  supposing  that  this  coalescence  of 
molecules  is  due  to  the  interaction  of  the  atoms,  or  possibly 
of  groups  of  atoms,  which  under  ordinary  conditions  would 
produce  molecules  of  olefine,  the  phenomenon  in  question 
is  brought  under  the  general  hypothesis  of  nascent  state. 
I  have  myself  shewn  that  bismuthic  oxide  (Bi2O5)  is  reduced 
to  bismuthous  oxide  (Bi2O3)  by  heating  in  hydrogen  at  a 
temperature  lower  than  that  at  which  hypobismuthic  oxide 
(Bi2O4)  is  reduced  to  the  same  final  state,  and  that  hypo- 
bismuthic oxide  is  reduced  to  hypobismuthous  oxide  (Bi2O2) 
at  a  temperature  lower  than  that  at  which  bismuthous  oxide 
undergoes  a  similar  change.  I  have  also  shewn  that  bismu- 
thic oxide  is  more  easily  and  completely  deoxidised  when 
heated  in  chlorine  than  bismuthous  oxide.  When  the  atoms 
composing  bismuthic  oxide  molecules  are  shaken  asunder,  the 
action  between  these  and  hydrogen,  or  chlorine,  proceeds 
until  a  stable  configuration  is  reached  ;  those  points  in  the 
molecular  series  known  as  hypobismuthic  and  bismuthous 
oxide  respectively,  are  passed  through  during  the  change,  but 
the  molecules  of  these  compounds  are  only  potentially,  not 
actually  formed :  when  however  these  molecules  have  been 
formed  before  chemical  action  begins,  a  higher  temperature 
must  be  reached  before  the  action  actually  occurs. 

42.  Whether  or  not  a  given  phenomenon  is  to  be  ex- 
plained by  the  particular  application  of  the  molecular  theory 
now  under  consideration,  must  be  decided  by  the  nature  of  that 
phenomenon.  Among  phenomena  which  are  usually  but  not 
invariably  explained  thus,  those  which  occur  in  the  decompo- 
sition of  acids  by  metals  are  of  great  importance. 

The  products  of  the  action  of  metals  on  sulphuric  and 
nitric  acid,  respectively,  have  been  already  broadly  stated. 
That  no  hydrogen  is  evolved  in  the  case  of  nitric  acid  is 
generally  sought  to  be  explained  by  assuming  that  the  hydro- 
gen atoms  are  seized  by  the  nitric  acid  and  oxidised  to  water, 
with  a  corresponding  reduction  of  the  acid  to  oxides  of  nitro- 
gen, nitrogen,  and  sometimes  ammonia. 


§  42]  ATOMIC  AND   MOLECULAR   SYSTEMS.  93 

Direct  proof  in  favour  of  this  hypothesis  has  been  given 
by  Gladstone  and  Tribe1,  who  have  shewn  that  when  a  small 
piece  of  magnesium  is  placed  in  a  large  excess  of  nitric  acid 
(strengths  I  :  I  and  I  :  2 — acid  to  water — were  employed)  the 
gas  at  first  evolved  consists  of  nearly  pure  hydrogen,  but 
that  oxides  of  nitrogen  are  very  quickly  produced.  The  same 
chemists2  have  established  a  close  relation  between  the  action 
on  sulphuric  and  nitric  acids  of  the  hydrogen  produced  by 
electrolysis  of  these  acids,  and  hydrogen  occluded  by  platinum 
or  palladium  ;  they  have  also  shewn  that  hydrogen  evolved 
by  the  action  of  the  copper  zinc  couple  is  very  analogous 
in  general  reducing  actions  to  hydrogen  occluded  by  platinum 
or  palladium. 

When  concentrated  nitric  acid  is  subjected  to  electrolysis 
no  hydrogen  is  evolved,  but  the  acid  is  reduced ;  when  more 
dilute  acid  is  used  hydrogen  is  evolved,  reduction  of  the  acid 
also  occurs,  and  the  more  rapid  the  electrolysis  the  greater 
the  quantity  of  hydrogen  evolved.  Concentrated  nitric  acid 
rapidly  acts  on  hydrogen  occluded  by  platinum  or  palladium, 
with  oxidation  of  the  hydrogen  and  reduction  of  the  acid. 
In  the  electrolysis  of  concentrated  sulphuric  acid  sulphur  is 
produced,  a  portion  of  the  hydrogen  formed  is  oxidised  and  a 
portion  escapes,  and  the  stronger  the  battery  power  the  greater 
is  the  quantity  of  hydrogen  evolved.  When  the  electrolysis  is 
extremely  slow,  no  hydrogen  is  evolved,  and  sulphur  dioxide 
is  produced  in  small  quantity  unmixed  with  free  sulphur. 
Hydrogen  occluded  by  palladium  or  platinum  also  reduces 
sulphuric  acid,  with  production  of  sulphur  dioxide  and  escape 
of  a  portion  of  the  hydrogen. 

Gladstone  and  Tribe  regard  the  metal  (platinum  or  palla- 
dium) present  in  their  experiments  as  instrumental  in  the 
chemical  change.  They  think  that  the  hydrogen  produced  is 
occluded  by  the  metal  and  again  given  off  to  the  acid,  and 
that  if  the  gas  is  produced  more  quickly  than  it  can  be 
occluded  the  excess  escapes  oxidation  by  the  acid :  it  is 


1  C.  S.  JfournalTrsaLa.  for  1879.  178. 

2  C.  S.  Journal  Trans,  for  1878.  139  and  306. 


94  CHEMICAL   STATICS.  [§  42 

probable  that  occluded  hydrogen  forms  a  compound  with  the 
occluding  metal,  and  that  therefore  hydrogen  coming  from 
this  source  is  for  the  most  part  in  the  nascent,  i.e.  atomic 
state.  Their  experiments  certainly  establish  the  fact  that 
maximum  reduction  of  either  acid  is  obtained  when  hydrogen 
is  evolved  therein  near  an  electro-negative  metal  ;  but  a 
comparison  of  the  results  with  occluded  and  electrolytically 
evolved  hydrogen  shews  that  the  reducing  action  of  the 
latter  on  sulphuric  acid  is  more  complete  than  that  of  the 
former. 

The  facts,  taken  as  a  whole,  concerning  the  action  of 
metals  on  nitric  acid  are  more  in  keeping  with  the  hypo- 
thesis of  the  intervention  of  nascent  hydrogen  than  with  the 
older  view,  which  regarded  the  various  gaseous  products  as 
direct  results  of  the  deoxidising  action  of  the  metal.  Indeed 
to  formulate  the  reaction  of  zinc  on  nitric  acid  on  the 
latter  hypothesis,  requires  that  nitric  acid  should  be  re- 
garded as  a  variable  compound  of  nitrogen  pentoxide  and 
water,  and  necessitates  considerable  skill  in  the  manipula- 
tion of  formulae1.  The  action  of  copper  on  concentrated 
sulphuric  acid  has  been  studied  by  Pickering2.  The  ease  with 
which  this  acid  undergoes  deoxidation  is  shewn  by  the  slow 
production  of  cuprous  sulphide  even  at  20°  ;  the  equation 


which  represents  the  change  as  consisting  in  deoxidation  of 
part  of  the  acid,  and  does  not  involve,  nor,  according  to 
Pickering's  experiments  allow,  an  intermediate  stage  wherein 
hydrogen  reacts  on  the  acid,  being  nearly  realized.  At 
higher  temperatures  sulphur  dioxide  is  evolved,  until  at 
about  270°  the  action  consists  entirely  of  a  change  which 
may  be  formulated  as 

Cu  +  2H2SO4=CuSO4+SO2 


1  Deville,  Compt.  rend.  70,  20  &  550;  or  in  abstract,  Watts's  Diet.  Suppl.  2, 
304.     See  also  Acworth  and  Armstrong,    C.  S.  Journal,  vol.  2.  for  1877,  54, 
et  seq. 

2  C.  S.  Journal  Trans,  for  1878.  112. 


§  42]  ATOMIC   AND    MOLECULAR   SYSTEMS.  95 

and  which  is   most  readily  explained    as  consisting  of  two 
parts  proceeding  simultaneously 

f(i)     Cu  +  H2SO4=CuS04+H2\ 
1(2)     H2-fH2SO4  =  2H2O  +  SO2J  ' 

Tin  and  lead  are  dissolved  by  hot  concentrated  sulphuric 
acid,  with  production  of  sulphates  and  evolution  of  hydrogen 
and  sulphur  dioxide,  sometimes  accompanied  by  sulphuretted 
hydrogen,  and  with  separation  of  sulphur.  With  more  dilute 
acid  tin  evolves  hydrogen,  and  as  temperature  is  increased, 
sulphuretted  hydrogen  also.  The  action  of  zinc  on  sulphuric 
acid  is  broadly  analogous  to  that  of  tin. 

Quantitative  analysis  of  the  products  of  reduction  of 
nitric  acid  by  magnesium,  zinc,  and  cadmium  respectively, 
shews  that  reduction  is  carried  furthest  by  magnesium,  and 
further  by  zinc  than  by  cadmium.  Now  the  '  heats  of  for- 
mation' (see  Chap.  IV)  of  the  oxides  of  these  metals  are, 
for  Mg  147,132,  for  Zn  88,244,  and  for  Cd  30,364  thermal 
gram-units,  hence  it  is  almost  certain  that  that  reaction  of 
metal  on  acid  in  which  the  greatest  amount  of  heat  is 
evolved  is  accompanied  by  the  greatest  reduction  of  acid. 

The  following  numbers  representing  quantities  of  heat 
evolved  in  the.  chemical  changes  formulated  were  obtained 
by  Thomsen  (see  Chap.  IV.). 

H2,  S,  O4,  aq.  =  2 10,760  gram-units  +. 

H,  N,  O3,aq.=  34,270  „  +. 

Zn,  H2SO4,  aq.  =  1 06,090  „  +. 

Zn,  2HNO3,  aq.  =  1 36,340  „  +. 

Berthelot  also  gives  the  thermal  value  of  21,500  gram- 
units  to  the  chemical  change 

HNO3  (dilute) +  8H  =  NH3  (dilute)  +  3H2O. 

From  these  numbers  we  should  expect  sulphuric  acid 
to  be  more  stable,  towards  heat,  than  nitric  acid,  and  we 
should  expect  the  action  of  zinc  on  these  acids  to  result 
in  a  more  complete  deoxidation  of  nitric  than  of  sulphuric 
acid. 

In  the  action  of  metal  on  nitric  acid  at  ordinary  tem- 
peratures, we  have  then,  an  unstable  acid,  a  considerable 


96  CHEMICAL  STATICS.  [§  42 

heat  evolution,  and  the  production  of  hydrogen  in  contact 
with  the  acid,  we  have  conditions  eminently  favourable  to 
deoxidation.  In  the  action  of  metal  on  dilute  sulphuric  acid, 
on  the  other  hand,  we  have  a  more  stable  acid  and  a  smaller 
heat  evolution,  consequently  the  hydrogen  escapes  un- 
changed ;  but  when  the  acid  is  so  concentrated  that  ad- 
dition of  heat  from  without  is  required. to  start  the  reaction, 
and  when  the  acid  is  therefore  in  a  condition  more  com- 
parable with  that  of  nitric  acid  at  ordinary  temperatures, 
a  portion  of  the  hydrogen  then  evolved  undergoes  oxi- 
dation at  the  expense  of  the  oxygen  of  the  acid.  If 
however  hydrogen  is  evolved — as  in  the  experiments  of 
Gladstone  and  Tribe — in  contact  with  concentrated  acid  at 
ordinary  temperatures,  a  part  of  this  hydrogen  is  always 
oxidised1. 

The  facts,  that  hot  sulphuric  acid  is  deoxidised  by  carbon, 
and  apparently  by  phosphorus  also2,  and  that  it  is  possible  by 
heat  alone  to  decompose  this  acid  into  sulphur  dioxide,  oxygen, 
and  water,  have  caused  some  chemists  to  regard  the  actions  of 
metals  on  this  acid  as  simply  cases  of  direct  deoxidation :  but 
it  seems  to  me  that  the  facts  enumerated — both  chemical  and 
physical,  with  regard  to  the  action  of  metals  on  this  acid  and 
on  nitric  acid — are  more  in  keeping  with  that  hypothesis 
according  to  which  hydrogen  plays  an  essential  part  in  the 
series  of  changes,  than  with  any  other  hitherto  advanced. 
There  may  be,  indeed  there  undoubtedly  is,  more  than  one 
process  of  chemical  change  resulting  in  the  deoxidation  of 
sulphuric  acid,  in  some  cases  direct  deoxidation  prepon- 
derates, in  others  hydrogen  plays  the  more  important  part. 

Experiments  recently  conducted  by  Thorpe3  on  the  re- 
ducing action  of  zinc,  magnesium  and  tin  on  acidulated 
solutions  of  ferric  sulphate,  shewed  that  whatever  condition 
tends  to  give  greater  chances  of  contact  between  the  hydro- 
gen produced  in  the  liquid  and  the  ferric  sulphate  in  solu- 

1  When  however  vapour  of  sulphuric  acid   mixed  with  hydrogen  is  passed 
through  a  hot  tube,  sulphuretted  hydrogen  is  produced. 

2  Cross,  C.  S.  Journal  Trans,  for  1879.  -253. 

3  C.  S.  Journal  Trans,  for  1882.  289. 


§§•  42,  43]        ATOMIC   AND   MOLECULAR   SYSTEMS.  97 

tion,  increases  the  rate  of  reduction ;  that  increase  of  the 
rate  at  which  hydrogen  is  evolved,  other  conditions  remaining 
constant,  is  accompanied  by  decrease  of  the  amount  of  re- 
duction in  unit  of  time ;  and  that  the  presence  of  certain 
salts,  e.g.  zinc  sulphate,  causes  a  decrease  in  the  rate  of 
reduction.  Thorpe's  results  also  established  a  distinct 
connection  between  the  nature  of  the  metal  used  and  the 
influence  on  the  rate  of  reduction  of  the  varying  conditions 
under  which  the  experiments  were  conducted. 

These  experiments,  and  indeed  all  experiments  on  the 
action  of  metals  on  acids,  emphasise  the  necessity  that  exists 
for  considering  all  the  reacting  substances  which  take  part  in 
a  process  of  reduction  by  hydrogen,  and  not  confining  atten- 
tion to  the  hydrogen  alone.  The  results  of  experiments  by 
Tommasi1  also  shew  this  need  :  Tommasi  found  that  potas- 
sium chlorate  was  not  deoxidised  by  hydrogen  evolved  by 
the  action  of  sodium-amalgam,  but  was  reduced  by  hydrogen 
evolved  by  the  action  of  zinc  on  diluted  sulphuric  acid, 
but  that  the  latter  agents  failed  to  remove  oxygen  from 
potassium  perchlorate. 

43.  The  conception  which  underlies  such  expressions  as 
nascent  actions,  action  of  nascent  hydrogen,  &c.,  is  that  im- 
plied in  the  distinction  drawn  between  atom  and  molecule. 
That  this  distinction  is  one  not  merely  of  terminology1  but 
based  on  actual  reactions,  is  rendered  apparent  by  the  results 
of  recent  experiments  by  Traube2  on  the  conditions  under 
which  hydrogen  peroxide — H2O8 — is  produced. 

Hydrogen  peroxide  has  been  very  generally  regarded  as 
oxidised  water;  Traube  says  it  is  rather  reduced  oxygen. 
The  production  of  hydrogen  peroxide  during  processes  of 
oxidation,  occurring  in  presence  of  water,  has  been  sought 
to  be  explained  by  assuming  that  the  oxidising  substance 
decomposes  oxygen  molecules,  retains  some  of  the  atoms, 
and  sets  the  others  free  under  conditions  favourable  to  the 
production  of  triatomic  molecules  of  ozone,  and  that  the 
ozone  thus  produced  then  reacts  on  water  molecules  and  con- 

1  See  especially  Pogg,  Beiblatter,  2.  205. 

2  Ber.  15.  659,  2421,  2434:  16.  1201. 

M.  C.  7 


98  CHEMICAL   STATICS.  [§43 

verts  these  into  molecules  of  hydrogen  peroxide.  Traube's 
hypothesis  regards  the  oxidising  substance  as  decomposing 
the  water  molecules  present,  withdrawing  oxygen  and  part  of 
the  hydrogen,  and  setting  free  the  remainder  of  the  hydrogen, 
which  thereupon  combines  with  oxygen  molecules  and  so  pro- 
duces hydrogen  peroxide. 

Thus,  the  production  of  hydrogen  peroxide  by  the  mutual 
action  of  zinc,  oxygen,  and  water  might  be  represented,  on  the 
first  hypothesis,  as  occurring  in  two  stages,  — 


W  \3ZnO+3H20  =  3Zn(OH)2, 
0)     3H20  +  03=3H202; 

and  on  the  second  hypothesis,  as  occurring  essentially  in  one 
stage,  thus,— 

(a)    3Zn  +  60H2  +  302=3Zn(OH)2  +  3H2<V. 

The  following  numbers,  representing  the  thermal  values  of 
various  changes,  some  of  which  may  occur  in  the  complete 
reaction  now  under  consideration,  are  taken  from  Naumann's 
Thermochemie*. 

[H2,  O]  =  68.36o  gram-units  +  .          [H2O,  O]  =  23,o7o  gram-units-. 
[H2,  O2,  aq]  =  45,290    „        „      +  .  [H2O2aq,  H2]  =  91,450     „        „      +. 


1  The  two  hypotheses  may  be  more  clearly  grasped  if  these   reactions  are 
represented  graphically  thus : 

O 
I.     (a)     Zn)       (OfO  | 

Zn  >  +  4  O  f  O  =  3ZnO  +  O  fcZnO  +  3H2O  =  3Zn  (OH)  J. 
ZnJ      (OfO 

":  O 

OHH 


o) 

VC 

rOH 
OH 

IH 

ro-o 

II.     Zn) 

lnj  +  ' 

OH 
OH 

:  H 
I  H 

j6-6  =  3Zn(OH)2+302H2 

OH 

i  H 

16  -6 

2  For  an  explanation  of  these  thermal  measurements  see/^x/,  chap.  IV.,  par.  1 18. 


§  43]  ATOMIC  AND   MOLECULAR   SYSTEMS.  99 

These  numbers  are  opposed  to  the  supposition  that  water 
should  be  readily  changed  into  hydrogen  peroxide  by  a  pro- 
cess of  direct  oxidation.  Traube's  results,  especially  those 
connected  with  his  experiments  on  electrolysis,  seem  to  shew 
that  neither  water  nor  hydrogen  can  be  directly  oxidised  to 
hydrogen  peroxide  (see  pp.  100 — 101). 

Certain  metals,  e.g.  zinc,  decompose  water  only  in  presence 
of  oxygen,  forming  hydroxides  and  hydrogen  peroxide  ;  other 
metals,  e.g.  sodium,  decompose  water  in  absence  of  oxygen, 
forming  hydroxides  and  evolving  hydrogen  ;  there  are  other 
substances,  for  instance  palladium  charged  with  hydrogen, 
the  action  of  which  on  water  shews  that  they  belong  to  the 
same  class  of  substances  as  zinc.  Traube  formulates  the 
actions  of  zinc  and  hydrogenised  palladium  (which  he  re- 
gards as  a  definite  compound  Pd2H)  on  water  in  presence  of 
oxygen  thus, — • 


OH  i  H)     (O  H-0 

Zn+  1+]  |  =Zn(OH),+  | 

OHiH          O  H-O 


Pda  i  H}      (OR  :  HI      (O  H-O 

•-H  I  ' 


- 

Pd2;H)      (OHjHj      (6  H-O 

When  the  quantity  of  hydrogen  peroxide  reaches  a  certain 
limit  a  secondary  action  begins,  resulting  in  the  decomposition 
of  the  peroxide  ;  thus  with  zinc, — 

Zn  +  H2O2=Zn(OH)2. 

Traube  thus  regards  the  formation  of  each  molecule  of 
hydrogen  peroxide  as  the  result,  of  the  action  of  two  atoms  of 
hydrogen  on  one  molecule  of  oxygen ;  he  does  not  suppose 
that  the  molecule  of  oxygen  is  shattered  and  that  its  con- 
stituent atoms  combine  with  the  atoms  of  hydrogen,  but  rather 
that  the  two  hydrogen  atoms  join  themselves  on  to  the  already 
formed  oxygen  molecule.  If  this  be  granted,  it  seems  to  follow 
that,  were  atoms  of  oxygen  presented  to  the  hydrogen  atoms 
as  they  escape  in  pairs  from  the  water  molecules,  water,  and 
not  peroxide  of  hydrogen,  would  be  produced.  Traube  says 
that  this  supposition  is  shewn  to  be  correct  by  the  reaction  of 

7—2 


100  CHEMICAL   STATICS.  [§  43 

zinc  on  an  aqueous  solution  of  potassium  nitrate ;  the  products 
of  this  action  are  zinc  hydroxide,  potassium  nitrite  and  water; 
thus, — 


OH 
Zn-f 
OH 


V 

Hj  : 


Zinc  has  no  action  on  an  aqueous  solution  of  potassium 
nitrite,  and  we  know  that  this  salt  in  the  solid  form  is  un- 
changed at  temperatures  whereat  potassium  nitrate  parts  with 
one-third  of  its  oxygen. 

If  the  conditions  of  the  preceding  action — that  viz.  of 
zinc  on  an  aqueous  solution  of  potassium  nitrate  in  presence 
of  oxygen — are  arranged  so  that  hydrogen  is  freely  evolved 
during  the  change  [this  can  be  most  readily  done  by  using 
zinc  and  iron  in  place  of  zinc  only],  then  some  of  the  potassium 
nitrite  is  further  reduced  with  production  of  ammonia.  It 
would  appeaf  then  that  in  certain  reactions,  when  hydrogen 
is  separated  from  water,  and  oxygen  is  separated  from 
another  compound  in  contact  with  the  water, — the  two  gases 
being  brought  within  the  sphere  of  mutual  action  in  the  pro- 
portion of  two  atoms  of  hydrogen  to  one  atom  of  oxygen, — 
water  is  produced  ;  but  that  when  the  hydrogen  and  oxygen, 
produced  as  before,  react  in  the  proportion  of  two  atoms  of 
hydrogen  to  one  molecule  (not  two  atoms)  of  oxygen,  hydro- 
gen peroxide  is  the  product. 

Traube  got  some  very  interesting  and  important  results 
from  experiments  on  the  electrolysis  of  water,  using  electrodes 
of  different  materials.  He  found  that  no  hydrogen  peroxide 
was  produced  when  the  electrodes  were  composed  of  one  of 
those  metals  which  readily  produce  hydrogen  peroxide  by 
their  action  on  water  and  oxygen  (or  in  some  cases  dilute  acid 
and  oxygen) ;  but  that  when  the  electrode  consisted  of  a 
metal  which  does  not  yield  hydrogen  peroxide  under  the 
conditions  named,  hydrogen  peroxide  was  formed,  in  greater 
or  less  quantity,  during  electrolysis. 

As  a  typical  member  of  the  latter  class  of  metals,  Traube 
chose  palladium.  When  palladium  is  charged  with  hydrogen 


§43]  ATOMIC  AND   MOLECULAR   SYSTEMS.  IOI 

and  made  the  positive  pole  of  the  battery,  no  hydrogen 
peroxide  is  produced,  but  the  oxygen  which  is  being  evolved  is 
absorbed  by  the  palladium  and  is  combined  with  the  occluded 
hydrogen  to  form  water.  When  however  the  hydrogenised 
palladium  is  made  the  negative  pole,  a  little  hydrogen  per- 
oxide is  produced  ;  and  the  quantity  of  this  compound  may 
be  considerably  increased  by  causing  bubbles  of  air  to  rise 
through  the  liquid  near  the  negative  pole.  If  however  no  air 
is  passed  through  the  water,  and  at  the  same  time  the  trans- 
ference of  oxygen  from  the  positive  pole  (where  it  is  being 
liberated)  through  the  liquid  to  the  negative  pole  is  me- 
chanically prevented,  no  hydrogen  peroxide,  or  only  a  trace 
of  this  compound,  is  produced.  Further,  if  hydrogenised 
palladium  is  made  the  positive  pole,  and  bubbles  of  air  are  at 
the  same  time  caused  to  rise  through  the  liquid  around  the 
pole,  a  little,  but  only  a  little,  hydrogen  peroxide  is  produced. 
Finally  if  the  electrodes  are  made  of  palladium  uncharged 
with  hydrogen  the  maximum  yield  of  hydrogen  peroxide  is 
obtained  (entirely  at  the  negative  pole)  by  arrariging  the  rate 
of  electrolysis  so  that  the  whole  of  the  hydrogen  produced  is 
occluded  by  the  palladium  ;  the  more  rapid  the  evolution  of 
hydrogen  from  the  liquid  the  smaller  is  the  quantity  of 
hydrogen  peroxide  produced1.  Now  it  is  generally  supposed 
that  the  greater  part  of  the  oxygen  or  hydrogen  liberated 
during  electrolysis  of  water  is  at  the  moment  of  its  pro- 
duction in  the  state  of  atoms,  and  that  the  greater  part  of  the 
oxygen  in  ordinary  air  is  composed  of  molecules ;  if  this  be 
granted,  it  follows  that  Traube's  experiments  establish  a 
marked  difference  between  the  reactions  of  oxygen  atoms  and 
oxygen  molecules  :  by  their  action  on  hydrogen  occluded  by 
palladium,  the  former  produce  water,  the  latter  produce 
hydrogen  peroxide ;  if  a  few  atoms  and  many  molecules  of 
oxygen  are  present  much  peroxide  and  little  water  are  the 
products,  while  if  many  atoms  and  few  molecules  of  oxygen 
are  brought  into  contact  with  the  hydrogen,  much  water  and 
little  peroxide  is  the  result. 

1  These  results  are  strictly  confirmatory  of  those  obtained  by  Gladstone  and 
Tribe  in  their  electrolytic  experiments  on  the  reduction  of  acids.     See  ante,  p.  93. 


102  CHEMICAL   STATICS.  [§  44 

44.     But  the  experiments  of  Traube  also  shew  that  the 
direction  and  final  goal  of  the  chemical  change  depends  not 
only  on  the  structure  of   the  particles  of  oxygen,  but   also 
on    the  source   and   conditions   of  supply    of  the  hydrogen. 
If  the  hydrogen  is  produced  by  rapid  electrolysis  little  per- 
oxide is  formed;  indeed  if  the  hydrogen  is  produced,  rapidly 
or  slowly,  by  electrolysis  with  carbon  poles  no  peroxide  is 
obtained.      The  chemical  nature,  and  the  masses,  of  all  the 
members  of  the   changing   system   influence  the   final   con- 
figuration.     The   importance   of  considering   the   conditions 
under  which  hydrogen  is  produced  when  we  are  attempting 
to  explain  any  of  the  phenomena  classed  together  as  those  of 
nascent  state,  is  emphasised  by  the  fact,  already  alluded  to, 
that  the  metals  which  decompose  water  in  absence  of  oxygen, 
do  not  give  rise  to  the  production  of  hydrogen  peroxide  by 
their    action  on  water  in  presence  of  oxygen:    for  instance, 
hydrogen  peroxide  is  never  produced  by  the  action  of  sodium 
on  water.    It  is  not  enough  then  that  oxygen  molecules  should 
be  present  in  contact  with  atoms  of  hydrogen  as  these  are 
liberated  from  water.     The  peroxide  results  from  the  mutual 
actions  and  reactions  of  the  three  substances,  metal,  water, 
oxygen ;    if  the  water   is  decomposed   by  the   metal  alone, 
hydrogen  is  evolved  rapidly  and  escapes  the  pursuit  of  the 
oxygen  molecules ;  the  peroxide  appears  to  be  a  product  of 
the  joint  action  of  the  metal  and  oxygen  on  the  molecules  of 
water. 

This  conception  of  a  joint  action  of  metal  and  oxygen 
may  be  carried  over  to  explain  some  of  the  phenomena  ex- 
hibited when  metals  and  acids  react.  Traube  seeks  to 
explain  many  of  these  reactions  in  this  way. 

Copper  does  not  remove  oxygen  from  an  aqueous  solution 
of  potassium  nitrate  as  zinc  does;  but  if  copper  is  brought 
into  contact  with  dilute  sulphuric  acid  in  presence  of  oxygen, 
hydrogen  peroxide  is  produced.  The  joint  action  of  copper 
and  potassium  nitrate  is  not  sufficient  to  decompose  water- 
molecules  ;  but  copper  and  oxygen  aided  by  a  little  sulphuric 
acid  suffice  to  complete  this  change.  The  action  in  question 
is  represented  thus  by  Traube, — 


§  44]  ATOMIC   AND   MOLECULAR   SYSTEMS.  103 

I'M) jo 

m  I  = 

I  HI      |O 


(OH  ;  H)      {O  H-O 

(a)     Cu  +  \         i      >  +  {  |  =  Cu(OH)2+ 

(OH  IH)      (O  H-O 


(b]  (when  a  certain  amount  of  H2O2  is  produced) 

Cu  +  H2O2  =  Cu(OH)2 

(c]  Cu(OH)2  +  H2SO4  =  CuSO4  +  2H2O. 

If  some  compound  which  is  readily  acted  on  by  hydrogen 
be  substituted  for  oxygen  in  this  series  of  changes,  then 
copper  and  dilute  sulphuric  acid  form  a  reducing  agent ; 
ferric  sulphate  e.g.  is  reduced  under  these  conditions  to  ferrous 
sulphate, — 


OH  |H 

I 
OH  :  H 


Similarly  the  action  of  copper  on  dilute  nitric  acid  would 
be  represented  thus,  —  • 


OH  ;  H) 

i      [  +  3(0  !  N02H)  =  3Cu(OH) 

OH  i  H)         i 

[but  3NO2H  rapidly  decomposes  to  give  HNO3  +  2NO  +  H2O]. 

As  thus  regarded,  these  actions  of  metals  on  acids  are 
complex  changes ;  at  one  stage  or  other  of  the  complete 
change  hydrogen  plays  an  important  part,  and  it  does  this  in 
virtue  of  being  itself  a  product  of  another  part  of  the  whole 
reaction.  Hydrogen  imported  from  without  the  system  fails 
to  accomplish  actions  which  are  brought  about  by  hydrogen 
generated  within  the  system,  provided  this  hydrogen  be  pro- 
duced at  the-  proper  rate,  and  under  conditions  generally 
favourable  to  the  action  it  is  to  perform. 

The  investigation  of  Divers1  '  On  the  production  of  hy- 
droxylamine  from  nitric  acid'  is  an  interesting  and  instructive 
example  of  the  need  of  considering  all  the  members  of  a  chang- 
ing system  in  attempting  to  find  an  explanation  of  the  change. 
Hydroxylamine  is  one  of  the  products  of  the  action  of  tin, 
zinc,  and  some  other  metals  on  nitric  acid;  ammonia  is  also 

1  C.  S.  Journal  Trans,  for  1883.  443. 


IO4  CHEMICAL   STATICS.  [§  44 

produced  in  these  reactions;  if  the  action  continues  for  some 
time  no  hydroxylamine,  but  only  ammonia  can  be  detected. 
Addition  of  hydrochloric  or  sulphuric  acid  causes  a  marked 
increase  in  the  yield  of  hydroxylamine.  Divers  shews  that 
the  production  of  hydroxylamine  by  the  direct  action  of 
tin,  &c.  on  nitric  acid  is  most  probably  preceded  by  separa- 
tion of  hydrogen  from  the  acid,  and  that  the  action  of  this 
hydrogen  on  another  portion  of  the  acid  is -the  immediate 
cause  of  the  formation  of  hydroxylamine.  He  also  regards 
his  experiments  (which  it  must  be  admitted  are  not  very 
numerous)  as  pointing  to  the  conclusion  that  the  reason  why 
silver,  mercury,  copper,  and  bismuth  do  not  produce  hydroxyl- 
amine or  ammonia,  when  they  act  on  nitric  acid,  is,  that 
these  metals  do  not  displace  hydrogen  in  nitric  acid,  but 
rather  combine  with  the  nitroxyl  and  hydroxyl  groups,  (NO2 
and  OH)  forming  nitrites  and  hydroxides  (MNO2  and  MOH), 
which  then  mutually  react  to  produce  nitrous  acid,  metallic 
nitrate,  and  water.  The  tin  and  zinc  metals,  on  the  other 
hand,  probably  directly  produce  metallic  nitrates,  the  sub- 
sequent formation  of  nitrites  being  due  to  reactions  between 
the  metal  and  its  nitrate.  Hydroxylamine  is  an  unstable 
substance ;  Divers  thinks  he  has  experimentally  shewn  that 
the  increase  in  the  yield  of  this  compound,  when  nitric  and 
hydrochloric  (or  sulphuric)  acids  act  on  tin,  &c.  over  the  yield 
obtained  by  the  action  of  nitric  acid  alone,  is  chiefly  due 
(i)  to  production  of  chloride,  or  sulphate,  of  hydroxylamine, 
both  of  which  salts  are  more  stable  than  the  nitrate,  (2)  to 
prevention,  by  the  hydrochloric  or  sulphuric  acid,  of  formation 
of  nitrous  acid,  which  readily  decomposes  hydroxylamine, 
and  (3)  to  production  and  maintenance  of  a  reducing  environ- 
ment (hydrogen)  around  the  hydroxylamine,  by  virtue  of 
direct  action  between  the  metal  and  the  second  acid.  Under 
these  circumstances  the  greater  part  of  the  hydroxylamine, 
produced  by  the  action  of  the  nitric  acid  on  the  metal,  re- 
mains undecomposed.  Divers  does  not  find  it  necessary  to 
suppose  that  the  second  acid  directly  supplies  hydrogen 
for  reduction  of  nitric  acid,  but,  at  the  same  time,  he  thinks 
that  this  reduction  is  indirectly  assisted  by  the  second  acid 


§  45]  ATOMIC  AND   MOLECULAR   SYSTEMS.  IO5 

by  virtue  of  a  reaction  between  it  and  the  metallic  nitrate, 
whereby  nitric  acid  is  continually  reproduced  in  the  solution. 
If  this  is  really  the  case,  then  it  may  very  well  be  that 
formation  of  hydroxylamine  is  increased  by  the  simultaneous 
production,  within  the  sphere  of  mutual  action,  of  hydrogen 
and  nitric  acid,  i.e.  by  the  presence  in  the  solution  of  nascent 
hydrogen  and  nascent  nitric  acid.  The  nature  of  the  second 
acid,  as  might  be  expected,  is  an  important  factor  in  the 
change  :  the  amount  of  water  present,  and  the  temperature  at 
various  stages  of  the  reaction  also  exert  marked  influence  on 
the  final  result. 

45.  The  expression  'nascent  action'  has  probably  been 
at  once  helpful  and  harmful  to  the  progress  of  chemistry. 
By  classing  under  a  common  name  many  phenomena  that 
might  otherwise  have  been  lost  in  the  vast  mass  of  facts  with 
which  the  science  has  to  deal,  the  expression  has,  I  think, 
done  good  service ;  but  in  so  far  as  its  use  has  tended  to 
prevent  investigation — for  it  is  always  easier  to  say  of  any 
unusual  reactions,  '  these  are  cases  of  nascent  action '  than  to 
examine  carefully  into  their  course  and  conditions — and  also 
in  so  far  as  it  has  favoured  the  impression  that  '  nascent ' 
hydrogen  or  *  nascent '  oxygen,  &c.  is  ordinary  hydrogen  or 
oxygen,  &c.  with  certain  indefinite  properties  which  are 
always  attached  to  the  hydrogen,  or  other  element,  when  in 
this  peculiar  condition,  the  use  of  the  expression  has,  I  think, 
been  unfavourable  to  the  best  interests  of  chemical  science. 

A  study  of  the  reactions  in  which  nascent  substances  play 
important  parts  appears  to  me  to  keep  before  the  student 
that  all-important  distinction  between  the  atom  and  the 
molecule  which  is  so  vital  in  chemical  considerations,  and  also 
to  draw  attention  in  a  marked  way  to  the  complexity  of  all 
chemical  changes.  We  find,  or  think  we  find,  that  when  atoms 
of  hydrogen  are  presented  to  another  substance  in  a  given 
chemical  reaction,  certain  definite  products  result ;  and  we 
are  apt  to  conclude  that  the  action  of  hydrogen  atoms  on 
this  substance  will  always  give  this  result ;  but  investigation 
discovers  that  not  only  the  course  of  the  reaction,  but  also  the 
final  configuration  of  the  changing  system,  is  dependent  on 


IO6  CHEMICAL  STATICS.  [§  46 

the  whole  previous  history  of  the  reacting  bodies.  Hydrogen 
as  it  is  produced  by  the  action  of  sodium-amalgam  appears  to 
possess  properties  different  from  those  which  characterise 
hydrogen  produced  by  the  action  of  zinc  on  dilute  sulphuric 
acid ;  attempts  to  explain  these  apparent  differences  lead  to 
fresh  researches  ;.  we  become  impressed  with  the  conviction  that 
chemistry  is  not  the  study  of  this  element  or  that,  regarded 
as  a  kind  of  matter  with  certain  fixed  physical  properties,  but 
that  processes  of  change  are  the  subject-matter  of  the  science, 
and  that  to  explain  any  one  of  these  we  must  take  into 
account  each  and  all  of  the  reacting  bodies,  and  each  and  all 
of  the  conditions  under  which  the  total  change  is  proceeding. 
If  the  expression  'nascent  action'  does  in  any  way  help  to 
emphasise  such  considerations  as  these,  I  think  it  ought  to  be 
retained  in  chemical  nomenclature. 


SECTION  II.     The  Dualistic  and  Unitary  Theories. 

46.  Partly  from  his  definition  of  element,  partly  from  his 
study  of  the  products  of  combustion  in  oxygen,  of  phosphor- 
us, carbon,  sulphur,  &c.,  Lavoisier  was  led  to  regard  every  salt 
as  formed  by  the  union  of  an  acid  with  a  radicle,  th4  latter 
being  itself  either  simple  or  compound.  ^ 

Davy  began  his  electro-chemical  researches  in  the  early 
years  of  the  present  century.  In  the  Philosophical  Transactions 
for  i  So/1,  and  in  his  Elements  of  Chemical  Philosophy*,  he 
regards  chemical  combination  as  accompanied  by  an  ex- 
change of  quantities  of  electricity  of  opposite  sign  between 
the  combining  bodies.  He  found  that  when  sulphur  and 
copper  are  rubbed  together  the  sulphur  is  negatively,  the 
copper  positively,  electrified;  and  that  when  the  sulphur  is 
heated  the  electrical  activities  become  more  apparent,  until 
the  sulphur  melts,  when  chemical  combination  occurs  and 
the  product,  copper  sulphide,  exhibits  neither  positive  or 

1  'On  some  chemical  agencies  of  electricity,'  p.  i. 

2  Collected  works^  vol.  iv.  (see  also  Ladenburg's  Ent-wickelungsgesehichte  der 
Chcmie,  pp.  75 — 81). 


§§46,47]        ATOMIC  AND   MOLECULAR   SYSTEMS.  107 

negative  electricity.  If  the  quantity  of  electricity  lost  in  the 
act  of  chemical  union  is  restored,  e.g.  by  the  passage  of  a 
current  through  the  compound  formed,  chemical  decom- 
position occurs  and  the  original  components  are  again  ob- 
tained. Davy  regarded  the  primary  cause  of  chemical  and 
electrical  effects  as  possibly  the  same  force ;  when  this  force 
is  exerted  between  masses  of  matter  electrical  phenomena 
result ;  when  it  is  exerted  between  the  smallest  particles  of 
bodies  chemical  phenomena  result.  Thus  in  his  Elements  of 
Chemical  Philosophy^  Davy  says,  '  Electrical  effects  are  ex- 
'  hibited  by  the  same  bodies  when  acting  as  masses,  which 
'  produce  chemical  phenomena  when  acting  by  their  particles ; 
'  it  is  not  therefore  improbable  that  the  primary  cause  of  both 
'  may  be  the  same,  and  that  the  same  arrangements  of  matter, 
'or  the  same  attracting  powers,  which  place  bodies  in  the 
'relations  of  positive  and  negative,  i.e.  which  render  them 
'attractive  of  each  other  electrically,  and  capable  of  com- 
1  municating  attractive  powers  to  other  matter,  may  likewise 
'  render  their  particles  attractive,  and  enable  them  to  combine, 
'when  they  have  full  freedom  of  motion.'  'That  the  de- 
'  composition  of  the  chemical  agents  is  connected  with  the 
'  energies  of  the  pile,  is  evident  from  all  the  experiments  that 
'  have  been  made ;  as  yet  no  sound  objection  has  been  urged 
'against  the  theory  that  the  contact  of  the  metals  destroys 
'  the  electrical  equilibrium,  and  that  the  chemical  changes 
'  restore  it ;  and,  in  consequence,  that  the  action  exists  as  long 
'as  the  decompositions  continue2.' 

47.  At  once  a  brilliant  theoriser  and  a  thorough-going 
experimenter,  Davy  did  not  attempt  to  found  a  general  scheme 
of  chemical  classification  on  his  electro-chemical  work.  This 
was  however  done  by  Berzelius,  who  developed  a  consistent 
and  definite,  although  narrow  theory  which  for  a  time  seemed 
to  explain  all  chemical  phenomena. 

1  Loc.  at.  pp.  119 — 120,  and  p.  125. 

2  It  is  interesting  to  observe  how  similar  this  view,   stated  by  Davy  in  the 
beginning  of  the  present  century,  is  to  the  latest  views  regarding  the  connection 
of  chemical  and  electrical  forces.     Compare  especially  Helmholtz's  '  Faraday  Lec- 
ture.'   (C.  S.  Journal  Trans,  for  1881,  277  et  seq :  see  particularly  pp.  300—302.) 
[See/torf,  Book  II. ] 


108  CHEMICAL   STATICS.  [§  4; 

All  chemical  actions  were  regarded  by  Berzelius  as  brought 
about  by  electrical  force1.  ' Die  Elektricitat...scheint  die  erste 
'  Thdtigkeits-  Ursache  in  der  ganzen,  uns  umgebenden  Natur  zu 
'  seinj  Electrical  actions,  according  to  Berzelius,  were  not  to 
be  described  as  consequences  of  contact,  or  of  mutual  action 
between  heterogeneous  bodies.  Each  elementary  atom,  he 
held,  is  endowed  with  two  kinds  of  electricity,  it  has  two 
electric  poles ;  but  these  poles  differ  in  strength,  so  that 
each  atom  considered  as  a  whole  is  characterised  as 
positively  or  negatively  electrified;  in  some  elementary 
atoms  positive  electricity  predominates  and  gives  a  positive 
character  to  the  whole  atom  ;  in  others  negative  electricity 
overpowers  the  positive.  When  a  positively  electrified  atom 
attracts  a  negatively  electrified  atom,  opposite  electricities 
neutralise  one  another,  but  the  electricities  formerly  masked 
in  the  separate  atoms  now  come  into  play,  and  so  the  new 
group  of  atoms,  as  a  whole,  exhibits  positive  or  negative 
electricity,  in  virtue  of  which  it  is  capable  of  chemically  com- 
bining with  other  atoms  or  groups  of  atoms.  But  as  the 
stronger  poles  are  first  neutralised,  it  follows  that  the  more 
complex  a  compound  is,  the  less  polarity  does  it  exhibit,  and 
hence  the  less  readily  does  it  combine  with  other  substances. 
Berzelius  moreover  regarded  the  quantity  of  electricity  on 
either  pole  as  to  some  extent  variable  with  variations  of 
temperature.  On  the  Berzelian  theory  atoms  are  regarded  as 
essentially  unipolar ;  one  polarity  so  predominates  over  the 
other  that  each  atom  acts  as  a  positively  or  negatively 
electrified  whole. 

The  electro-chemical  properties  of  oxidised  compounds, 
Berzelius  taught,  depend  chiefly  on  the  unipolarity  of  the 
electro-positive  radicles  they  contain.  Of  two  oxides,  that 
which  contains  the  more  electro-negative  radicle  is  generally 
itself  electro-negative ;  thus  sulphuric  acid  (regarded  as  SO3) 
is  electro-negative  to  all  metallic  oxides,  because  sulphur  is 
itself  electro-negative  to  all  metals ;  on  the  other  hand  the 
oxides  of  potassium  and  sodium  are  electro-positive  to  all 
other  oxides  (excepting  those  of  caesium  and  rubidium)  be- 

1  Lehrbuch  (ist  Ed.),  in.  part  i.  p.  77. 


§47]  ATOMIC  AND   MOLECULAR   SYSTEMS. 

cause  potassium  and  sodium  are  themselves  electro-positive 
to  all  other  elements1  (except  caesium  and  rubidium). 

Polarity  and  chemical  affinity  are  closely  connected  in  the 
system  of  Berzelius :  the  '  specific  unipolarity' 2  however  does 
not  alone  determine  the  greater  or  less  affinity  of  one  atom 
for  another.  Some  atoms  have  a  more  intense  polarity  than 
others  and  therefore  exhibit  a  greater  striving  (' Bestreben')  to 
neutralise  the  electricity  divided  between  their  poles,  in  other 
words,  have  a  greater  affinity  for  a  given  substance  than 
other  atoms. 

Chemical  affinity  appears  to  have  been  regarded  by  Ber- 
zelius as  nearly  synonymous  with  intensity  of  atomic  polarity3. 
Thus,  oxygen  combines  with  sulphur  rather  than  with  lead, 
although  oxygen  and  sulphur  have  the  same  unipolarity  (viz. 
negative) ;  but,  the  Berzelian  view  asserts,  the  positive  pole  of 
the  sulphur  atom  neutralises  more  negative  electricity  on  the 
oxygen  atom  than  can  be  neutralised  by  the  positive  pole  of 
the  lead  atom. 

Double  decompositions  were  readily  explained  in  terms  of 
this  theory:  ' Every  chemical  action,'  says  Berzelius4,  'is  an 
'electrical  phenomenon  depending  on  the  electrical  polarity 
'  of  the  particles ;  everything  that  appears  to  be  due  to  the 
'  action  of  affinity  is  caused  by  the  possession  by  some  bodies 
'  of  an  electrical  polarity  stronger  than  that  of  others.  If  the 
'compound  AB  is  decomposed  by  the  substance  C which  has 
'  a  greater  affinity  for  A  than  B  has,  then  C  must  possess  a 
'  more  intense  electrical  polarity  than  B ;  on  this  account 
'  there  results  more  complete  neutralisation  between  A  and  C 
'than  between  A  and  B....  If  two  bodies,  AB  and  CD,  so 

1  An  important  deduction  made  from  these  considerations  is,  that  as  oxygen 
occurs  both  in  markedly  electro-positive  and  electro-negative  compounds,  and  as 
acids  are  as  a  group  electro-negative,  oxygen  cannot  be  the  acidifying  element,  as 
Lavoisier  said  it  was. 

2  Spedfische  Unipolaritdt.     Berzelius,  loc.  cit.  p.  73. 

3  This  might  perhaps  be  regarded  as  equivalent  to  the  modern  conception  of 
higher  and  lower  potential ;  as  if  one  atom  might  have  a  smaller  electrical  charge 
but   at  a  higher  potential  than  another,  and   would  therefore   exhibit  greater 
chemical  affinity  than  the  other. 

4  Lehrbuch  (ist  Ed.),  m.  part  i.  p.  77. 


1 10  CHEMICAL   STATICS.  [§48 

'react  as  to  produce  two  new  bodies,  AD  and  BC,  it  follows 
'  that  the  electrical  polarities  are  better  neutralised  in  the 
'  latter  pair  of  bodies  than  in  the  former/ 

48.  On  the  basis  of  this  theory  Berzelius  raised  the  struc- 
ture of  the  dualistic  chemistry,  which  asserted  that  every 
compound,  whether  simple  or  complex,  must  be  constituted 
of  two  parts,  of  which  one  is  positively,  and  the  other  negatively 
electrified. 

The  doctrine  of  dualism  is  thus  introduced  by  Berzelius1 : 
'  If  these  electro-chemical  conceptions  are  just,  it  follows  that 
'every  chemical  compound  is  dependent  on  two  opposing 
1  forces,  positive  and  negative  electricity,  and  on  these  alone ; 
'and  that  every  compound  must  be  composed  of  two  parts 
'held  together  by  their  mutual  electro-chemical  reactions. 
'  Therefore  it  follows  that  every  compound  body,  whatever  be 
'the  number  of  its  constituents,  can  be  separated  into  two 
'parts,  whereof  one  is  positively  and  the  other  negatively 
'electrified.  Thus,  for  example,  sodium  sulphate  is  put 
'  together,  not  from  sulphur,  oxygen,  and  sodium,  but  from 
'sulphuric  acid  and  soda,  which  again  can  themselves  be 
'separated  into  positive  and  negative  constituents.  So  also 
'alum  cannot  be  regarded  as  immediately  built  up  from  its 
'  elements,  but  must  rather  be  looked  on  as  the  product  of  a 
'  reaction  between  sulphate  of  alumina  and  sulphate  of  potash, 
'the  former  acting  as  a  negative,  the  latter  as  a  positive 
'  element2.' 

In  support  of  his  theory  Berzelius  appealed  to  the  facts  of 
electrolysis.  A  solution  of  sodium  sulphate  containing  a  little 
blue  vegetable  colouring  matter  is  electrolysed  ;  the  colouring 
matter  is  reddened  around  the  positive  electrode  and  rendered 
more  distinctly  blue  around  the  negative.  What  can  this 
experiment  teach  but  that  the  salt  is  separated  by  the  electric 
current  into  alkaii  and  acid  ?  And  can  the  inference  be 
avoided  that  the  salt  is  composed  of,  or  contains  in  itself, 

1  Lehrbuch,  loc.  cit.  p.  79. 

2  See   also   Berzelius,    Theorie   des  proportions    chimiques,   et    de  ^influence 
chimique  de  Felectricite  dans  la  nattire  inorganique ',   3rd  Ed.  Paris,  1835.     Also, 
for  a  condensed  account  of  the  electro-chemical  theory  of  Berzelius,  see  Laden- 
burg,  loc.  cit.  pp.  89  —  93. 


§  49]  ATOMIC   AND    MOLECULAR   SYSTEMS.  I  I  I 

these  two  compound  radicles,  soda  (Na2O)  and  sulphuric 
acid  (SO3)  ?  All  salts  were  to  be  regarded  as  dualistic  struc- 
tures. Given  the  composition  of  a  salt,  a  dualistic  formula — or 
rather  a  series  of  formulae — was  at  once  devised  for  it.  The 
following  formulae  were  employed  by  various  dualistic  chemists 
to  express  the  structure  of  acetic  acid, — 

(i)  C4H603.  H20  (2)  C4H604.  H2  (3)  C4H60.  02.  H2O 

(4)  (C2H6)C203.  H,0  (5)  (C^CjO,.  H2  (6)  (C3H6O)CO2.  H2O 

(7)  C4H8 .  04  (8)  C2H4 .  02  (9)  C4H6O2 .  H2O2 
(10)  C4H2.04H6. 

To  choose  the  proper  formula  from  such  a  chaos  was  a  task 
possible  only  for  one  whose  foible  was  omniscience.  That 
formula  which  had  the  weight  of  authority  on  its  side  was 
accepted  as  correct. 

49.  Lavoisier  had  regarded  oxygen  as  the  'acidifying 
principle'.  Hydrochloric  acid  was  undoubtedly  an  acid  sub- 
stance, therefore,  in  accordance  with  the  dictum  of  Lavoisier, 
it  contained  oxygen.  Davy's  study  of  this  compound,  and 
of  its  analogue  hydriodic  acid,  nevertheless  established  the 
fact  that  an  acid  can  exist  which  contains  no  oxygen.  The 
further  fact,  that  so  many  of  the  oxides — then  called  acids — 
exhibited  acid  properties  only  in  presence  of  water,  led  Davy 
to  the  belief  that  very  many  acids  contain  hydrogen.  Shak- 
ing off  the  trammels  of  that  older  philosophy  which  regarded 
the  introduction  of  undefined  'principles '  as  affording  expla- 
nations of  natural  phenomena,  Davy  said  that  acids  are  not 
characterised  by  the  invariable  presence  of  any  one  element, 
but  that  certain  compounds  of  very  diverse  elements  belong 
to  this  group1. 

Dulong2  in  1815  further  advanced  Davy's  conception  of 
acids  by  recognising  no  essential  difference  between  those 
acids  which  contain  oxygen  and  those  which  do  not. 
Lavoisier's  acid  theory  was  not  however  generally  aban- 
doned until  many  years  later. 

1  For  an  account  of  the  important  work  of  Davy  on  the  non-oxygenised  acids, 
and  the  arguments  of  his  opponents,  see  Ladenburg,  loc.  cit.  pp.  81 — 87. 

2  Mem.  deVAcad.  1813 — 15,  p.  198,  and  Schiveiggcr1  s  Journal,  17.  229. 


112  CHEMICAL   STATICS.  [§§  50,  51 

In  1837 — 38  Liebig1,  following  up  Graham's  work  on 
phosphoric  acid2,  distinctly  recognised  the  existence  of  're- 
placeable hydrogen'  in  acids,  whether  oxy-acids  or  acids 
containing  no  oxygen,  and  defined  salts,  as  compounds  be- 
longing to  the  same  class  as  acids,  and  formed  by  putting 
metal  in  place  of  an  equivalent  quantity  of  hydrogen  in  acids3. 

This  view  of  the  structure  of  salts  was  altogether  opposed 
to  the  dualistic  theory  of  Berzelius. 

50.  Another  severe  blow  was  inflicted  on  the  prevailing 
theory  by  Faraday's  researches  on  electrolytic  decompositions. 

Faraday  shewed  that  the  quantities  of  various  elements 
set  free  from  different  electrolytes,  by  the  same  electric 
current,  were  chemically  equivalent  to  one  another:  thus 
for  each  two  parts  by  weight  of  hydrogen  set  free  from 
water,  there  were  obtained  16  parts  of  oxygen,  78^2  parts 
of  potassium,  63*5  parts  of  copper  from  persalts  and  127 
parts  of  copper  from  protosalts.  But  the  affinities  of  the 
atoms  of  the  various  electrolytes  were  undoubtedly  different 
in  each  combination.  According  to  Berzelius,  the  quantity 
of  electricity  collected  on  any  group  of  atoms  is  greater,  the 
greater  the  mutual  affinity  of  these  atoms  ;  but  Faraday's 
experiments  shewed,  that  in  so  far  as  this  electricity  was 
measurable  by  electrolytic  decomposition,  (and  that  at  least 
comparative  measurements  should  be  thus  obtained  followed 
from  the  terms  of  the  dualistic  theory  itself),  the  quantity 
of  it  was  in  no  way  dependent  on  the  affinities  of  the  com- 
bining atoms4. 

51.  A  bold  and  partially  successful  attempt — such  an 
attempt  as  could  be  made  only  by  a  man  of  preeminent 
power — had  been  made  by  Berzelius  to  found  chemical  clas- 
sification on  the  study  of  composition  alone,  almost  wholly 
divorced  from  the  study  of  function,  or  power  of  doing. 

1  Compt.  rend.  5.  863  (with  Dumas):  and  Annalen,  26.   113,  see  especially 
p.  181. 

2  Phil  Trans,  for  1833.  253. 

3  See,  in  connection  with  acid  generally,    Laurent,    Chemical  Method,   pp. 

39-45- 

4  See  Helmholtz,  'The  Faraday  Lecture.'     C.  S.  Journal  Trans,  for  1881. 

pp.  284 — 6. 


§51-]  ATOMIC  AND   MOLECULAR   SYSTEMS.  113 

As  his  authority  became  greater,  Berzelius  led  chemistry 
further  from  the  only  true  path  by  which  she  could 
advance,  that  namely  wherein  experiment,  and  reasoning 
on  experimental  data,  go  hand  in  hand.  And  yet  no  single 
chemist  has  enriched  the  science  by  the  addition  of  so  great 
a  mass  of  laboriously  and  accurately  determined  experi- 
mental data  as  he.  The  intense  concentration  of  his  great 
intellectual  powers  upon  one  view  of  chemical  phenomena 
led  Berzelius  to  disparage  the  reasoning  of  those  who  sought 
to  view  these  phenomena  from  standpoints  other  than  his 
own. 

Among  those  who  recalled  chemistry  to  the  true  scien- 
tific method,  Dumas,  Laurent,  and  Gerhardt  stand  pre- 
eminent. 

In  I8391  Dumas  described  trichloracetic  acid,  obtained  by 
the  action  of  chlorine  on  acetic  acid.  The  new  compound, 
although  containing  chlorine  in  place  of  hydrogen,  was  a 
monobasic  acid,  and  resembled  acetic  acid  in  its  general 
reactions.  Dumas  said  there  are  certain  types  in  organic 
chemistry  which  are  maintained  even  when  an  equal  volume 
of  chlorine,  bromine,  or  iodine,  is  put  in  the  place  of  hydro- 
gen in  the  parent  substance8. 

Berzelius,  and  the  defenders  of  the  dualistic  chemistry, 
violently  opposed  the  idea  that  the  electrically  negative 
chlorine  could  be  substituted  for  the  positive  hydrogen, 
and  the  identity  of  type  yet  be  maintained.  In  Dumas' 
succeeding  papers3  the  conception  of  types  was  more  fully 
developed.  All  bodies  containing  the  same  number  of  equi- 
valents of  simple  substances,  combined  in  a  similar  manner, 
and  exhibiting  broad  analogies  of  properties,  were  regarded 
as  belonging  to  the  same  type.  Such  bodies  were  also,  as  a 
rule,  simply  related  to  one  another  by  reactions  of  formation 
and  decomposition  : — thus  acetic  and  chloracetic  acids  ;  chlo- 
roform, bromoform,  and  iodoform  ;  ethylene  and  its  chloro- 


1  Compt.  rend.  8.  609,  and  Annalen,  32.  roi. 

2  Compt.  rend.  8.  621. 


3  Annalen,  33.  259:  35.  129  (with  Stas),  and  289  (with  Peligot);  or  Compt. 
rend.  9.  813,  and  10.  149. 

M.  C.  8 


114  CHEMICAL   STATICS.  [§52 

derivatives,  &c.,  belonged  to  the  same  types,  or  as  Dumas 
said  to  the  same  'natural  families'.  Dumas  regarded  car- 
bonyl  chloride  as  derived  from  carbonic  anhydride  by  substi- 
.tuting  one  oxygen  by  two  chlorine  atoms — thus  COO  gives 
COC12;  this  was  utterly  opposed  to  the  dualistic  view,  ac- 
cording to  which  the  formula  of  carbonyl  chloride  was 
written  CO .  CC14,  because  every  compound  must  be  com- 
posed of  two  parts,  one  of  which  is  electrically  positive  and 
the  other  negative. 

52.  The  new  school  of  chemists  naturally  opposed  the 
conception  of  compound  radicles,  a  conception  too  closely 
associated  with  those  dualistic  theories  they  were  leaving  be- 
hind, to  find  favour  in  their  sight.  But  these  chemists  found 
that  unless  substitution  of  simple  atoms  by  groups  of  atoms 
were  regarded  as  possible,  identity  of  type  could  not  be 
maintained  through  groups  of  compounds  undoubtedly  be- 
longing to  the  same  natural  family. 

Inasmuch  as  the  new  chemistry  based  its  claims  to  re- 
cognition on  an  appeal  to  actual  reactions,  it  was  impossible 
that  it  should  long  refuse  to  recognise  the  conception  of 
compound,  as  well  as  simple,  radicles,  without  proving  false 
to  its  own  method.  Liebig  and  Wohler,  in  their  researches 
on  oil  of  bitter  almonds,  explained  the  observed  reactions 
of  the  compounds  they  obtained  by  assuming  the  existence 
of  the  compound  radicle  benzoyl  (—  CUH10O2)  in  these  bodies 
(see  Annalen,  3.  249). 

But  what  are  these  compound  radicles  which  the  chemists 
who  upheld  the  unitary  system  were  obliged  to  recognise, 
equally  with  their  opponents  who  supported  a  dualistic  theory? 
Are  they  definite  groups  of  atoms  always  existing  as  such 
in  compound  molecules,  or  are  they  only  convenient  methods 
of  expressing  and  generalising  reactions  ? 

As  chemistry  advanced,  compound  radicles  came  to  be 
generally  recognised  as  certain  groups  of  atoms,  in  com- 
pound molecules,  which  remain  undecomposed  throughout 
a  series  of  reactions  undergone  by  those  compounds1.  Thus 

1  See  especially  Laurent's  Chemical  Method,  pp.  276 — 300.     Also  Ladenburg, 
loc.  cit.  pth  and  xoth  Lectures. 


§  53]  ATOMIC    AND   MOLECULAR   SYSTEMS.  1 1  5 

we  find  Kekule  in  1857  citing  the  case  of  sulphuric  acid, 
H2SO4,  which  when  acted  on  by  zinc  gives  ZnSO4,  and 
may  therefore  be  said  to  contain  the  radicle  SO4,  but  when 
acted  on  by  phosphorus  pentachloride,  the  compound  SO2C12 
is  produced,  hence  the  acid  may  be  said  to  contain  the 
radicle  SO,1. 

53.  The  conception  of  types  was  destined  to  bear  much 
fruit.  Let  us  briefly  trace  its  development. 

Liebig  and  Dumas  had  regarded  salts  as  substituted 
metallic  derivatives  of  acids,  they  had  spoken  of  a  quantity 
of  metal  as  taking  the  place  of  an  equivalent  quantity  of 
hydrogen  ;  Dumas  had  even  ventured  to  regard  the  negative 
chlorine  as  capable  of  replacing  an  equivalent  amount  of  the 
positive  hydrogen.  In  doing  this,  these  chemists  had  returned 
to  the  old  conception  of  equivalents — too  much  forgotten  by 
the  Berzelian  school — as  quantities  to  be  determined  by  the 
study  of  reactions,  but  they  had  given  this  conception  fresh 
life  by  engrafting  on  to  it  the  notion  of  natural  families 
or  types. 

In  writing  the  formulae  of  sulphates,  selenates  and  chro- 
mates,  as  MO  .  SO3 ;  MO  .  SeO3 ;  and  MO  .  CrO3,  Berzelius  had 
undoubtedly  recognised  the  principle  of  types ;  but  so  long  as 
this  principle  was  dominated  by  the  necessities  of  the  dual- 
istic  system  it  was  unfruitful.  The  idea  of  the  chemically 
reacting  unit  as  one  whole,  one  structure  with  parts  capable 
of  replacement  by  other  parts  without  the  necessary  de- 
struction of  the  building,  gave  meaning  to  what  was  before 
but  a  form  of  words. 

From  its  earliest  beginnings  to  its  present  form  the  theory 
of  types  has  been  interwoven  with  the  atomic  theory ;  with- 
out the  latter,  the  former  had  never  had  being.  If  the  value 
of  a  scientific  idea  is  to  be  measured  by  its  fruitfulness,  then 
is  Dalton's  New  System  of  Chemical  Philosophy  the  most  im- 
portant work  yet  produced  by  any  chemist. 

Now  if  the  reacting  unit  of  any  substance  is  possessed 
of  a  definite  atomic  structure,  only  those  bodies  can  be  said 

1  The  modern  development  of  the  conception  of  compound  radicle  will  be 
better  understood  by  considering  pars.  70  to  74  in  Section  4  of  this  chapter. 


Il6  CHEMICAL  STATICS.  [§53 

to  belong  to  the  same  type,  or  natural  family,  whose  re- 
acting units  are  built  on  a  similar  atomic  plan  :  but  our 
only  method  of  discovering  similarity  of  structure  is  by  study- 
ing reactions ;  hence  only  those  bodies  which  are  charac- 
terised by  similarity  of  chemical  function  ought  to  be 
classified  under  the  same  type1.  And  as  modification  of 
structure  has  been  recognised  as  not  necessarily  implying 
destruction  of  type,  it  follows  that  those  quantities  of  radi- 
cles, simple  or  compound,  are  equivalent,  which  can  perform 
similar  functions  in  similarly  constituted  compounds. 

At  last  a  method  of  chemical  classification  has  been  found 
by  Dumas,  Liebig,  Gerhardt,  and  Laurent  which,  when  more 
fully  developed,  will  reconcile  those  who  regard  composition 
as  all  important,  with  those  for  whom  function  is  supreme; 
which  will  preserve  the  fundamental  conception  of  equiva- 
lent, but  interpret  it  in  terms  of  the  wider  theory  of  atoms; 
and  which  will  recognise  the  connection,  while  yet  empha- 
sising the  importance  of  the  difference  between  the -atom  of 
Dalton  and  the  molecule  of  Avogadro. 

But  in  its  development  the  theory  of  types  must  neces- 
sarily be  largely  modified.  Classification  by  types  cannot  be 
final  in  a  science  which  has  advanced  so  far  towards  be- 
coming an  abstract  science  as  chemistry. 

'  By  the  classification  of  any  series  of  objects  is  meant 
'the  actual,  or  ideal,  arrangement  together  of  those  which 
'  are  like  and  the  separation  of  those  which  are  unlike  ;  the 
'  purpose  of  this  arrangement  being,  primarily,  to  disclose  the 
*  correlations  or  laws  of  union  of  properties  or  circumstances, 
'  and,  secondarily,  to  facilitate  the  operations  of  the  mind 
'  in  clearly  conceiving  and  retaining  in  the  memory  the  "  cha- 
'racter  of  the  objects  in  question2".' 

Those  'properties  or  circumstances' which  are  correlated 
must  be  such  as  are  really  characteristic  of  the  objects  clas- 
sified, they  must  be  essential  properties  of  these  objects,  not 
mere  surface  appearances ;  they  must  be  capable  of  accurate 

1  See  especially  Laurent's  Chemical  Method,  pp.  -298 — 300. 

2  W.  Stanley  Jevons  (modifying  the  words  of  Huxley),  Principles  of  Science, 
2.  p.  348. 


§§  53>  54]        ATOMIC   AND   MOLECULAR   SYSTEMS.  1 1/ 

definition,  and  at  the  same  time  of  fairly  easy  recognition; 
and  that  property — or  properties — chosen  as  the  mark  of 
a  class  must  belong  to  all  the  members  of  that  class. 

But  the  properties  of  a  type  are  necessarily  somewhat 
vague :  properties  regarded  by  one  observer  as  essentially 
belonging  to  the  type  may  by  another  be  regarded  as  acci- 
dental ;  a  given  substance  may  possess  so  many  of  the 
properties  of  the  type  as  at  one  time  suffices  to  ensure  its 
admission  into  the  class,  but  at  a  future  time  new  proper- 
ties may  be  discovered  which  necessitate  the  removal  of  the 
substance  to  a  class  whose  type  shews  considerable  diverg- 
ence from  that  under  which  the  substance  was  originally 
placed. 

The  very  elasticity,  and  even  vagueness,  of  the  theory 
of  types  ensured  it  an  important  place  in  the  development 
of  chemical  science. 


SECTION   III.     Equivalency  of  atoms. 

54.  Dualism  had  reigned  supreme,  but  only  because 
it  was  despotic  ;  when  the  rebellion,  headed  by  Dumas,  once 
got  a  footing  the  fate  of  the  older  theory  was  sealed.  The 
new  system  succeeded  because  it  was  not  too  systematic. 

In  attempting  to  preserve  unity  of  type  through  large 
series  of  compounds,  the  builders  of  modern  chemistry  were 
obliged  to  make  free  use  of  the  conception  of  compound 
radicles  as  substituting  simple  radicles ;  they  thus  became 
familiarised  with  the  general  notion  of  each  radicle  pos- 
sessing a  definite  substituting  power. 

In  1852  Frankland1  extended  this  conception  to  the 
atoms  of  the  elementary  bodies;  in  1855  Odling2  introduced 
the  use  of  dashes  placed  over  the  atomic  symbols  to  express 
what  he  called  '  the  replaceable,  or  representative,  or  substitu- 

1  Phil.  Trans.  142.  417,  see  especially  p.  440. 

-  C:  S.  Journal,  1.  i.  (The  recognition  of  two  'replaceable  values'  for  the 
iron  atom,  and  other  atoms,  shews  the  close  connection  between  the  theory  then 
coming  into  existence  and  the  older  theory  of  equivalents.) 


Il8  CHEMICAL  STATICS.  [§54 

'  tion  value '  of  these  atoms,  he  also  recognised  that  an  ele- 
mentary atom  may  have  more  than  one  'replaceable  value'. 
Odling  applied  this  fruitful  conception  to  the  formulae  of 
many  salts,  especially  the  phosphates,  and  succeeded  in 
shewing  analogies  until  then  overlooked. 

The  inherent  fascination  of  the  idea  of  compound  radicle 
may  be  realised,  by  considering  that  in  less  than  twenty  years 
after  Dumas'  discovery  of  the  chloracetic  acids — which  marks 
the  beginning  of  the  revolt  against  the  compound  radicles 
of  dualism — Kekule1,  and  independently  of  him,  Couper2 
(in  papers  of  the  greatest  importance)  found  it  necessary 
to  recall,  chemists  to  the  consideration  of  elementary  atoms 
as  being  the  true  units  by  the  combinations  of  which  all 
compound  molecules  are  built  up,  and  by  whose  properties 
those  of  the  compounds  are  determined.  Couper  criticised 
Gerhardt's  development  of  types,  objecting  to  the  vagueness 
of  the  idea  as  a  basis  for  classification  ;  and  especially  op- 
posing Gerhardt's  opinion  that  the  molecular  constitution 
of  bodies  can  never  be  ascertained  by  chemists.  *  Would 
'  it  not  be  rational/  says  Couper,  '  in  accepting  this  veto  to 
'renounce  chemical  research  altogether?'  This  dictum  of 
Gerhardt  is  to  be  traced,  in  Couper's  opinion,  to  the  overdue 
employment  of  compound  radicles,  to  forgetting  that  these 
can  have  no  properties  which  are  not  'a  direct  consequence  of 
'  the  properties  of  the  individual  elements  of  which  they  are 
'  made  up,'  and  hence  to  endowing  these  radicles  with  some 
'  unknown  and  ultimate  power  which  it  is  impossible  to 
'  explain.5  Returning  then  to  a  study  of  the  elements,  Couper 
finds  chemical  affinity  as  a  property  inherent  in,  and  common 
to  them  all;  he  distinguishes  'affinity  of  kind'  and  'affinity 
'  of  degree ;'  applying  the  latter  to  carbon,  he  cites  the 
oxides  CO  and  CO2  (in  his  notation  C2O2  and  C2O4),  the 
former  expressing  the  first,  the  latter  the  second  and  last 
degree :  CO2  is  '  the  ultimate  affinity,  or  combining  unit 
'  for  carbon.' 


1  Annalen  (1857),  104-  129- 

2  Phil.  Mag.  (1858)  [4],  16.  104, 


§§  54»  55]        ATOMIC  AND   MOLECULAR   SYSTEMS,  1 19 

Kekule  in  1857,  and  more  especially  in  a  paper  published 
in  March  I8581 — a  paper  the  importance  of  which  can  hardly 
be  overrated — distinguishes  more  clearly  than  Couper  'affi- 
'nityofkind'  from  'affinity  of  degree;'  or  rather  he  distin- 
guishes chemical  affinity  from  what  he  calls  the  '  basicity  of 
1  atoms!  both  conceptions  being  needed,  he  says,  for  the 
explanation  of  chemical  combinations,  Kekule  clearly  dis- 
tinguishes— and  this  distinction  has  been  too  much  forgotten 
in  recent  developments  of  chemical  theory — between  equi- 
valent weights  of  elements,  and  equivalency  (or  basicity)  of 
elementary  atoms ;  he  shews  that  the  new  theory  deals 
with  definite  entities,  called  atoms,  having  defined  properties, 
and  not  with  '  unit  weights,'  and  that  it  is  these  atoms  which 
he  proposes  to  compare  as  to  their  substituting  power  for  the 
hydrogen  atom.  Having  shewn  that  one  atom  of  carbon, 
so  far  as  our  knowledge  goes,  is  never  combined  with  more 
than  four  atoms  of  hydrogen  in  a  compound  molecule,  Kekule 
also  shews  that  two  atoms  of  carbon  do  not  bind  to  them- 
selves more  than  six  atoms  of  hydrogen,  three  atoms  of 
carbon  not  more  than  eight  atoms  of  hydrogen,  and  so  on. 

The  tetravalency  of  the  carbon  atom,  and  the  power 
which  two,  or  more,  atoms  of  carbon  possess  of  binding  them- 
selves together  in  a  molecule,  are  enunciated  by  Kekule  in 
this  paper,  which  forms  the  foundation  stone  of  the  modern 
theory  of  '  atom-linking2.' 

Kekule  and  Couper  insisted,  that  if  a  definite  theory  of 
the  connections  between  properties  and  structure  of  com- 
pounds is  to  be  obtained,  it  must  be  based  on  the  study  of  the 
combining  powers  of  the  elementary  atoms :  '  The  whole  is 
*  simply  a  derivative  of  its*  parts,'  said  Couper. 

55.  A  theory  which  shall  attempt  to  explain  the  atomic 
structure  of  compound  molecules,  must,  in  the  present  state 


1  Annateii,  106.  129. 

2  In  comparing  Couper's  paper  with  Kekule's  it  may  be  well  to  notice  how 
Couper  attempts  to  trace  a  close  connection  between  the  basicity  of  atoms  and 
chemical  affinity;   his  statements  are  here  much  vaguer  than  Kekule's,  yet  this 
dynamical    method  of  regarding   'valency'  at  the   very  outset   of  the  theory  is 
important. 


120  CHEMICAL   STATICS.  [§§  55,  56 

of  knowledge,  confine  itself  to  gaseous  bodies.  We  do  not 
know  how  to  determine  the  relative  weights  of  the  mole- 
cules of  solid  or  liquid  substances.  We  have  reason  to  believe 
that  the  molecular  structure  of  a  mass  of  solid  or  liquid 
is  much  more  complex  than  that  of  a  mass  of  a  gaseous 
substance ;  no  generalisations  have  yet  been  made  regarding 
molecular  phenomena  of  solids  or  liquids  comparable  with 
those  which — under  the  names  of  the  laws  of  Boyle,  Charles, 
and  Avogadro — have  been  made  regarding  molecular  phe- 
nomena of  gases.  We  must  recognise  the  limits  within  which 
a  theory  of  atomic  structure  can  assist  advance;  if  it  be 
pushed  too  far  it  will  become,  with  some  a  dogma,  with 
others  a  thing  to  be  scorned. 

Considering  these  molecular  formulae  HC1,  H2O,  H3N, 
H4Si,  it  is  seen  that  one  atom  of  chlorine  is  combined  with 
one  atom  of  hydrogen  in  the  molecule  HC1,  that  one  atom  of 
oxygen  is  combined  with  two  atoms  of  hydrogen  in  the  mole- 
cule H2O,  that  one  atom  of  nitrogen  is  combined  with  three 
atoms  of  hydrogen  in  the  molecule  H8N,  and  that  one  atom 
of  silicon  is  combined  with  four  atoms  of  hydrogen  in  the 
molecule  H4Si.  Considering  the  molecular  formulae  C1H, 
Cl2Hg,  Cl3Bi,  and  Cl4Sn,  it  is  seen  that  one  atom  of  hydrogen 
is  combined  with  one  atom  of  chlorine,  one  atom  of  mercury 
with  two  atoms  of  chlorine,  one  atom  of  bismuth  with  three 
atoms  of  chlorine,  and  one  atom  of  tin  with  four  atoms  of 
chlorine,  in  various  compound  molecules. 

These  facts  may  be  expressed  by  saying  that  the  atoms  of 
oxygen  and  mercury  are  divalent,  the  atoms  of  nitrogen  and 
bismuth  are  trivalent,  and  the  atoms  of  silicon  and  tin  are 
tetravalent,  i.e.  so  far  as  the  data  at  present  before  us  are  con- 
cerned, the  atom  of  oxygen  or  of  mercury  can  combine  with 
two  atoms  of  hydrogen  or  of  chlorine,  the  atoms  of  nitrogen 
and  bismuth  can  combine  with  three  atoms  of  hydrogen  or 
chlorine,  &c.,  to  form  compound  molecules. 

56.  But  these  terms  monovalent,  divalent,  &c.,  must  be 
more  strictly  defined. 

If  the  table  on  pp.  37 — 40  is  examined,  it  will  be  found 
that  all  molecules  of  gases  containing  only  atoms  of  hydrogen, 


§  56]  ATOMIC  AND   MOLECULAR   SYSTEMS.  121 

[fluorine]1,  chlorine,   bromine,   iodine*,  and  thallium,  contain 
two  atoms  ;  the  molecules  in  question  are,  — 

H2,  C12,  Br2,  I2,  [HF]1,  HC1,  HBr,  HI,  IC1,  T1C1. 

These  then—  H,  [F]1,  Cl,  Br,  I,T1—  are  monovalent  atoms, 
i.  e.  atoms  which  combine  each  with  one  other  atom  to  form 
molecules. 

Now  if  we  tabulate  the  formulae  of  molecules  composed 
of  two  elements,  one  of  which  is  H,  F,  Cl,  Br,  I,  or  Tl,  we 
have  this  result,  — 


HgCl  :  OH2,  OC12,  SH2,  SeH2,  TeH^  CdBr2,  ZnCl2,  HgCl2,  HgBr2, 
HgI2,  SnCl2,  PbCl2  :  BF3,  BC13,  BBr3,  NH3,  PH3,  PC13,  AsH3, 
AsCl3,  AsI3,  SbCl3,  BiCl3,  InCl3  :  CH4,  CC14,  SiF4,  SiCl4,  SiI4,  TiCl4, 
ZrCl4,  VC14,  SnCl4,  SnBr4,  UBr4,  UC14  :  PF5,  NbCl6,  TaCl6,  MoCl5, 
WCI6  :  WCL,  [A12C16,  Al2Br6,  A12I6,  Fe2Cl6,  Cu2Cl2,  Ga2Cl6,  Sn2Cl4.] 

Omitting  the  formulae  in  brackets,  —  inasmuch  as  these 
molecules  contain  more  than  a  single  atom  of  the  element 
other  than  H,  F,  Cl,  Br,  I,  or  Tl,  —  the  following  arrangement 
expresses  the  results  of  this  tabulation. 

Monovalent  atoms  If,  F,  Cl,  Br,  /,  77. 

I.    Atoms   which   combine  with   one   monovalent   atom  to   form  a 

compound  molecule    Hg. 
II.     Do.      two  do,        O,  S,  Se,  Te,  Cd,  Zn,  Hg,  Sn,  Pb. 

III.  Do.      three          do.        B,  N,  P,  As,  Sb,  Bi,  In. 

IV.  Do.      four  do.         C,  Si,  Ti,  Zr,  V,  Sn,  U. 
V.     Do.      five  do.         P,  Nb,  Ta,  Mo,  W. 

VI.     Do.      six  do.        W. 

When  it  is  said  that  one  atom  is  combined  with  another, 
direct  action  and  reaction  between  these  atoms  in  the  mole- 
cule is  assumed.  In  saying,  therefore,  that  one  bismuth  atom 

1  Mallet  \_Amer.  Chem.  Journal  3.  189]  has  shewn  that  at  low  temperatures 
the  molecule  of  hydrofluoric  acid  must  be  represented  by  the  formula  H2F2;  at 
higher  temperatures  however  the  formula  HF  represents   the  molecule  of  this 
gas.     It  is  possible  that  hydrofluoric  acid  is  a  'molecular  compound'  at  low 
temperatures  (see  Section  5  of  the  present  chapter)  ;  determinations  of  the  density 
of  this  gas  for  a  considerable  range  of  temperature   would  throw  light  on  this 
question. 

2  The  iodine  molecule  is  probably  monatomic  at  very  high  temperatures,  and 
so  forms  an  exception  to  this  statement.     (See  ante,  p.  42,  par.  20.) 


122  CHEMICAL   STATICS.  [§57 

is  combined  with  three  chlorine  atoms  in  the  molecule  BiCl3, 
it  is  assumed  that  the  bismuth  atom  acts  directly  upon  (and  is 
acted  on  by)  each  chlorine  atom.  This  is  not  proved  by  the 
formula  BiCl3 :  it  might  be  assumed  that  the  bismuth  atom 
acts  indirectly  on  one  chlorine  atom  through  another  chlorine 
atom ;  but,  considering  that  all  molecules  which  contain  a 
single  atom  of  chlorine  contain  only  one  other  atom,  the 
simplest  hypothesis  is  that  the  bismuth  atom  is  trivalent  in 
the  molecule  BiCl3. 

57.  A  monovalent  atom  has  been  defined  to  be  an  atom 
which  combines  .with  one  other  atom  to  form  a  .molecule. 
The  best  definition  of  a  di-,  tri-,  &c.-valent  atom  would 
probably  be, — an  atom  which  combines  with  two,  three,  &c. 
other  atoms  to  form  a  molecule1;  but  the  definition  generally 
adopted  is, — an  atom  which  combines  with  two,  three,  &c. 
monovalent  atoms  to  form  a  molecule. 

According  to  this  definition  the  valency  (or  equivalency, 
or  quantivalence)  of  an  elementary  atom  is  a  number  which 
tells  the  number  of  monovalent  atoms  (i.e.  atoms  of  H,  F,  Cl, 
Br,  I,  or  Tl)  with  which  the  given  atom  combines  to  form 
a  molecule.  Of  the  26  elements  (not  including,  that  is, 
the  typical  monovalent  atoms)  in  the  foregoing  six  series, 
four,  viz.  P,  Sn,  W  and  Hg,  are  found  each  in  two  series. 
Recalling  the  fact  that  an  element  has  frequently  more  than 
one  equivalent  number,  and  remembering  that  we  are  now 
endeavouring  to  arrange  the  elementary  atoms  in  groups,  the 
members  of  each  of  which  are  to  be  equivalent  among  them- 
selves, this  variation  in  the  valency  of  the  atoms  of  these 
four  elements  is  not  surprising. 

The  fact  that  the  number  of  monovalent  atoms  combining 
with  some  of  the  other  elementary  atoms  is  variable,  necessi- 
tates an  addition  to  the  definition  of  valency,  which  may  now 
run  thus.  The  valency  of  an  elementary  atom  is  a  number 
which  tells  the  maximum  number  of  monovalent  atoms  (i.e. 

1  In  Frankland's  paper  already  referred  to  [Phil.  Trans,  142.  417-]  this 
definition  is  apparently  adopted,  'no  matter  what  the  character  of  the  uniting 
atoms  may  be,  the  combining  power  of  the  attracting  element is  always  satis- 
fied by  the  same  number  of  these  atoms'  (p.  440). 


§§  57>  58]        ATOMIC   AND   MOLECULAR   SYSTEMS.  123 

atoms  of  H,  F,  Cl,  Br,  I,  or  Tl)  with  which  the  given  atom 
combines  to  form  a  molecule.  Of  the  four  atoms  in  the 
arrangement  on  p.  12 1  whose  valency  is  expressed  by  more 
than  one  number,  two, — mercury  and  tungsten, — combine 
with  an  odd  or  an  even  number  of  monovalent  atoms,  one, — 
tin, — combines  with  an  even  number  only,  and  one, — phos- 
phorus,— combines  with  an  odd  number  only,  of  monovalent 
atoms,  to  form  compound  molecules. 

If  those  molecules  which  contain  only  H,  F,  Cl,  Br,  I, 
or  Tl  atoms  and  the  group  of  atoms  methyl  (CH3)  or  ethyl 
(C2H5)  are  tabulated1,  it  is  found  that  such  molecules  contain 
two  atoms,  that  is  if  it  be  permitted  to  apply  the  term  '  atom ' 
to  the  group  (CH3)  or  (C2H5).  These  groups  may  therefore 
be  regarded  as  monovalent.  By  tabulating  the  formulae  of 
molecules  composed  of  two  'elements,'  one  of  which  is  methyl 
or  ethyl,  we  find  that  lead  is  to  be  added  to  the  list  of  those 
elements  the  valency  of  whose  atoms  varies  but  is  always 
expressed  by  an  even  number2. 

Molecules  which  do  not  contain  monovalent  atoms  cannot 
be  employed  for  decisively  fixing  the  valencies  of  atoms, 
although  arguments  for  or  against  a  certain  valency  may  be 
drawn  from  consideration  of  such  molecules. 

58.  From  the  data  already  given,  the  oxygen  atom  is 
said  to  be  divalent :  now  it  might  be  argued  that  if  a  mole- 
cule is  found  containing  one  atom  of  oxygen  and  one  atom 
of  another  element,  the  second  atom  is  divalent ;  if  a  mole- 
cule is  found  containing  two  atoms  of  oxygen  and  one  atom 
of  another  element,  the  second  atom  is  tetravalent,  &c.  The. 
molecules  CO  and  CO2  are  cases  in  point.  The  latter  (CO2) 
has  been  often  used — e.g.  by  Kekule  in  his  paper  of  1858 — 
to  prove  the  tetravalency  of  the  carbon  atom.  Let  the 
valency  of  an  atom  be  represented  by  one,  two  or  more 
straight  lines  proceeding  from  the  atomic  symbol,  thus  H  — , 

—  O— ,   —  Bi— ,   &c.,  then  the  formula    O  =  C  =  O    expresses. 
I 

1  These    molecules    are    (CH3)H,    (CH3)F,     (CH3)C1,     (CH3)Br,    (CH3)I, 
(C2H5)H,  (C2H5)C1,  (C2H5)Br,  (C2H5)I. 

2  The  molecules  in  question  are  Hg(CH3)o,  Hg(CoH5)2,  Zn(CH3)2,  B(CH3)3, 
Sb(C2H5)3,  Si(C2H5)4,  Sn(CaH,)4,  Pb(CH3)4." 


124  CHEMICAL  STATICS.  [§  59 

the  supposed  fact  that  the  carbon  atom  is  tetravalent  in  the 
molecule  CO2.  But  this  formula  assumes  that  there  is  direct 
action  between  the  carbon  and  each  oxygen  atom,  but  not 
between  the  oxygen  atoms  themselves;  this  cannot  be  ac- 
cepted as  proved.  Further,  the  formula  appears  to  assume 
a  double  action  of  some  kind  between  the  carbon  and  oxygen 
atoms,  such  double  action  being  represented  by  the  double 
lines  =. 

59.     Let  us  consider  the  meaning  of  these  lines  ( — ). 

The  carbon  atom  is  tetravalent,  i.e.  the  carbon  atom 
combines  with  not  more  than  four  monovalent  atoms :  but  the 
carbon  atom  has  four  equivalencies,  or  four  valencies,  or  four 
bonds,  or  four  units  of  affinity — each  of  these  expressions  is  in 
common  use — what  does  this  mean l  ? 

(1)  It  cannot  mean  that  the  force  of  affinity  of  a  carbon 
atom  is  divided  into  four  parts  within  that  atom,  for  '  force ' 
has   no  meaning  apart  from  two  or  more  reacting   bodies : 
force  is  a  name  given  by  one  of  the  parties  to  a  transaction, 
but  a  transaction  involves  at  least  two  transacting  parties. 
The  force  between  a  carbon  atom  and  another  atom  must 
vary  with  external  conditions,  probably  with  the  distance,  the 
mass,  and  the  chemical  nature  (a  vague  term,  but  perhaps  as 
good  as  can  be  given  at  present)  of  both  atoms. 

(2)  The  carbon  atom  has  four  equivalencies,  or  four  units 
of  affinity.     This  cannot  mean  that  four  parts  of  the  carbon 
atom  are  chemically  active,  and  the  other  parts  inactive :  such 
a  hypothesis  leads  at  present  to  contradictions  (see  appendix 
to  Section  4) ;  moreover  in  the  present  state  of  knowledge  it  is 
inadvisable  to  hazard  hypotheses  as  to  the  inner  structure  of 
atoms  in  order  to  explain  chemical  phenomena.    Atoms  may 
not  be  homogeneous,  but  at  present  they  are  the  ultimate 
particles  to  be  considered  in  chemical  changes. 

(3)  The   expression   under   consideration    cannot    mean 
that  the  chemical  energy  of  a  carbon  atom  is  divided,  or  is 

1  A  paper  of  the  greatest  importance  entitled  '  Ueber  die  Vertheilung  der 
Atome  in  der  Molekel,'  by  W.  Lessen,  appeared  in  Annalen,  204.  265.  I  have 
made  free  use  of  this  paper  in  the  present  chapter.  (See  also  Claus,  Ber.  14. 
432  ;  and  Lessen,  ibid.  760.) 


§  59]  ATOMIC   AND   MOLECULAR   SYSTEMS.  12$ 

always  divisible  into  four  parts.  What  is  to  be  the  unit  of 
chemical  work  ?  the  mass  of  matter  fixed  by  a  given  atom  ? 
where  then  is  the  equivalency  between  one  atom  of  oxygen 
with  the  mass  16  and  two  atoms  of  chlorine  with  the  mass  71  ? 
Let  a  carbon  atom  combine  with  four  hydrogen  atoms,  the 
total  chemical  energy  of  the  atoms  disappears ;  let  a  carbon 
atom  combine  with  two  atoms  of  oxygen,  the  total  chemical 
energy  of  the  atoms  again  disappears  :  but  if  the  carbon  atom 
possesses  four  ( units  of  affinity/  the  oxygen  atom  two  '  units 
of  affinity,'  and  the  hydrogen  atom  one  '  unit  of  affinity/  the 
heats  of  formation  of  the  two  compound  molecules  ought  to  be 
equal.  But  the  differences  between  the  heats  of  formation  of 
carbon  compounds  shew  that  the  expression  '  the  carbon  atom 
'has  four  units  of  affinity'  cannot  mean  that  the  chemical 
energy  of  the  carbon  atom  is  divisible  into  four  parts,  unless 
indeed  the  unit  of  affinity  is  variable,  and  is  varied  for  each 
combination  of  carbon  with  other  atoms1. 

(4)  The  carbon  atom  has  four  equivalencies.     Can  this 
mean  that  the  atom  exerts  force  in  four  directions  ?     A  so- 
called  'valency'  is  then  a  direction.     But  there  is  no  force 
exerted  till  the  mutual  atomic  transaction  begins ;  the  carbon 
atom  considered  alone  has  therefore  no  '  valencies/     Take  the 
molecule  CO,  force  is  exerted  by  the  carbon  on  the  oxygen 
atom ;   the  remaining  '  valencies '  are  sometimes  said  to  be 
'mutually  satisfied/  i.e.  on  the  present  hypothesis,  the  carbon 
atom  in  the  molecule  CO  exerts  force  in  two  directions  on 
itself;    but  here  again  we  have  the  hypothesis  of  the  non- 
homogeneity  of  the  carbon  atom,  and  the  existence  of  active 
and  inactive  parts  in  that  atom. 

(5)  In  the  vibration  of  a  carbon  atom  there  are   four 
points,  at  each  of  which  mutual  action  can  occur  between  this 
atom  and  another  atom.    On  this  supposition,  a  '  double  link ' 
would    mean   that    mutual    action   occurs   between   the   two 
atoms  thus  linked  at  two  of  these  positions;  e.g.  the  formula 
O  =  C  =  O  means,  that  in  performing  a  vibration  the  carbon 
atom  acts  twice  on  (and  is  twice  acted  on  by)  each  oxygen 

1  For  a  view  analogous  to  this  see  appendix  to  Section  4  of  the  present 
chapter,  par.  98. 


126  CHEMICAL   STATICS.  [§§  59,  60 

atom.  But  if  so,  surely  a  ' double  link'  would  imply  mole- 
cular stability,  whereas  it  frequently  means  the  reverse1. 

The  theory  of  units  of  affinity,  or  valencies2,  or  bonds,  has 
been  carried  too  far.  It  appears  at  first  sight  to  give  a  dy- 
namical explanation  of  the  structure  of  molecules,  but  it  has 
forgotten  the  two-sidedness  of  atomic  transactions ;  it  appa- 
rently affords  a  means  of  measuring  atomic  forces,  but  it  has 
used  a  unit,  undefined  except  as  a  quantity  changeable  at 
pleasure ;  it  appears  to  simplify  chemical  formulae,  but  it  has 
really  made  them  harder  to  understand  by  grafting  on  to 
the  definite  conception  of  atom  the  vague  and  unnecessary 
notion  of  '  bond.'  When  the  molecule  has  been  analysed  and 
shewn  to  be  an  atomic  structure,  the  theory  of  bonds  has 
attempted  to  reconstruct  the  building,  not  by  putting  together 
the  parts  into  which  it  had  been  separated,  but  by  the  use 
of  new  untried  material  called  'bonds/  the  properties  of  which 
— if  it  has  any — are  unknown. 

The  theory  of  '  valencies '  has  gone  too  far  because  it  has 
not  gone  far  enough  ;  it  has  not  clearly  distinguished  the 
atoms  of  Dalton  from  the  equivalents  of  Wollaston.  In 
1858  Kekule  recalled  chemists  to  the  consideration  of  ele- 
mentary atoms  as  the  fundamental  units  of  which  chemical 
compounds  are  built  up;  twenty- two  years  later  Lessen  has 
recalled  the  followers  of  Kekule  to  the  same  all-important 
fact. 

60.  Let  us  turn  back  to  the  facts  on  which  was  based 
a  classification  of  many  elementary  atoms  into  monovalent, 
divalent,  tri,  tetra,  penta,  and  hexvalent  groups  (p.  121). 

The  atom  of  tin  is  divalent  in  the  molecule  SnCl2 :  the 
atom  of  tin  is  tetravalent  in  the  molecule  SnCl4 :  these  state- 
ments are  more  shortly  expressed  by  the  graphic  formulae 

Cl 
I 

Cl  —  Sn  —  Cl,    and     Cl  — Sn  — Cl 
I 
Cl 

1  On  the  subject  of  'double-bonds'  see  also  appendix  to  Section  4  of  this  chapter. 

2  It   is   important   to   distinguish  between  the  expressions  *  valency1  and  'a 
valency.' 


§  66]  ATOMIC  AND   MOLECULAR   SYSTEMS.  12? 

respectively ;  a  line  (-•-)  joining  two  atoms  is  used  to  denote 
direct  action  and  reaction  between  these  atoms. 

As  thus  interpreted,  the  statement/ a  given  atom  is  mono-, 
'  di-;  tri-,  &c.  valent  in  this  or  that  molecule/  has  a  definite 
and  defined  meaning. 

Lessen  (loc.  cit.)  insists  on  the  necessity  of  naming  the 
molecule  in  which  a  given  atom  occurs,  when  the  valency  of 
that  atom  is  stated.  Such  a  general  statement  as  'the  atom 
'  of  carbon  is  tetravalent '  must  be  taken  as  meaning  '  one  atom 
'of  carbon,  so  far  as  we  know  at  present,  is  never  directly 
' combined  with  more  than  four  other  atoms,'  or  'four  is  the 
'  maximum  number  of  atoms  which  can  come  within  the 
'  "binding-sphere"  of  a  carbon  atom  in  any  molecule'  (Lossen). 
The  special  statements,  *  in  the  molecule  of  carbon  dioxide 
'  the  carbon  atom  is  divalent/  '  in  the  molecule  of  carbon 
'  monoxide  the  carbon  atom  is  monovalent/  mean,  that  in  one 
molecule  the  carbon  atom  acts  directly  on — and  is  acted  on 
by — two  other  atoms,  and  in  the  other  molecule  on  one  other 
atom  ;  or,  in  the  first  molecule  there  are  two  atoms,  and  in 
the  second  molecule  one  atom,  within  the  binding-sphere  of 
the  carbon  atom. 

As  illustrations  of  this — Lossen's — way  of  regarding  va- 
lency, let  us  take  the  molecule  POC1S.  'In  this  molecule  the 
'phosphorus  atom  is  trivalent:'  the  formula 

.      ci  — P  — O  — Cl 

I 

ci 

expresses  this  statement  completely ;  there  is  direct  action, 
and  reaction,  between  the  phosphorus  atom  and  three  other 
atoms,  and  as  the  chlorine  atom  is  always  monovalent,  one  of 
the  three  atoms  must  be  oxygen.  But  it  is  sometimes  said, 
'  in  phosphoryl  chloride  the  phosphorus  atom  is  pentavalent/ 
and  the  formula 

Cl 

I 
Cl  — P  =  0 

I 
Cl 


128  CHEMICAL   STATICS.  [§  60 

is  used  as  expressing  this  statement.  But  this  is  equivalent 
to  saying,  the  phosphorus  atom  has  five  'bonds/  three  of 
which  are  '  satisfied '  by  chlorine  atoms,  and  two  by  an  oxy- 
gen atom.  The  objections  to  such  a  statement  have  been 
already  considered.  Assuming  that  there  is  direct  action, 
and  reaction,  between  the  phosphorus  atom  and  each  of 
the  other  atoms  comprising  the  molecule  POClff,  Lossen's 
formula  would  express  the  structure  of  this  molecule  thus 

Cl 

Cl  — P  — O, 
t 
Cl 

This  formula  would  be  translated  into  the  corresponding 
system  of  nomenclature  by  saying,  'in  this  molecule  the 
'  phosphorus  atom  is  tetravalent.' 

Again,  the  formulae  of  carbon  monoxide  and  dioxide  are 
generally  written  <  C  =  O  and  O  =  C  =  O  respectively,  and 
the  carbon  atom  is  said  to  be  tetravalent  in  both,  i.e.  in  each 
the  carbon  atom  has  four  '  bonds,'  in  CO  two  are  satisfied  by 
oxygen  and  two  satisfy  one  another,  in  C(\  on  the  other 
hand  each  oxygen  atom  satisfies  a  pair  of  bonds.  Lossen 
would  write  the  formulae  of  these  molecules  as  C  —  O  and 
O  — C  — O,  and  say,  the  carbon  atom  is  monovalent  (i.e.  acts 
directly  on  a  single  atom)  in  the  first,  and  divalent  (i.e.  acts 
directly  on  two  atoms)  in  the  second1.  The  first  pair  of 
formulae  almost  necessarily  implies  that  the  force  between 
the  carbon  and  the  oxygen  atoms  in  CO  is  equal  to  that 
between  the  carbon  and  each  oxygen  atom  in  CO2,  and  this 
dynamical  conception  is  strengthened  by  the  use  of  such 
expressions  as  the  'bonds  are  satisfied/  &c.  No  such  assump- 
tion is  made  by  Lossen's  formulae.  Most  probably  the  force 
between  any  pair  of  atoms  varies  in  different  molecules  in 
which  this  pair  of  atoms  is  present ;  whether  this  is  so  or  not, 
and  if  it  is  so,  whether  the  force  is  greater  in  molecule  a  than 

1  Of  course  CO2  may  be  written  O  -  C  -  O  ;  whether  there  is  or  is  not  direct 


action  between  the  oxygen  atoms  must  be  determined  by  a  general  study  of  the 
chemical  habitude  of  the  molecule. 


§  6l]  ATOMIC  AND   MOLECULAR   SYSTEMS.  1  29 

in  molecule  b  (or  vice  versa],  is  a  dynamical  question  which 
cannot  be  solved,  at  present,  by  the  theory  of  valency;  it 
is  a  question  outside  of  this  theory  ;  and  it  is  surely  better 
to  recognise  this,  and,  especially  in  view  of  the  masses  of 
new  facts  and  new  hypotheses  which  are  showered  on 
chemists,  to  make  the  theory  of  vajency  definite,  even  if 
this  be  done  by  narrowing  its  scope. 

61.  But  it  is  said,  CO  is  an  unsaturated,  CO2  a  saturated 
molecule.  What  then  it  may  be  asked  is  a  saturated  molecule  ? 
A  saturated  molecule,  it  is  usually  answered,  is  one  which 
exhibits  no  tendency  to  combine  directly  with  other  mole- 
cules, or  atoms  ;  an  unsaturated  molecule  on  the  other  hand 
is  ready  to  form  additive  compounds.  Now  the  molecule  CO 
readily  combines  with  C12  to  form  the  new  molecule  COClg1, 
therefore  CO  is  an  unsaturated  molecule  :  to  this  it  may  be 
answered,  with  Lossen,  that  as  Cl^  readily  combines  with  CO, 
C12  is  an  unsaturated  molecule.  Definitions  so  indefinite  as 
'  readiness  or  unreadiness  to  form  additive  compounds  '  do 
not  help  us  to  understand  the  apparently  precise  formulae,  e.g. 
<C  =  O  and  O=C  =  O,  in  which  these  definitions  are  ex- 
pressed. The  expressions  '  unsaturated  molecule  '  and 
'molecule  with  -free  bonds'  are  frequently  used  as  synony- 
mous ;  if  we  can  attach  a  precise  meaning  to  the  latter 
expression  we  shall  have  gained  the  definition  we  are  seeking. 
The  molecule  C2H4  very  easily  combines  with  bromine  to  form 
C2H4Br2,  that  is  to  say,  QH4  acts  as  an  unsaturated  molecule, 
and  therefore  contains  '  free  bonds  '  ;  but  the  generally  adopted 

CH2 
formula,     ||      ,  represents   the  two  carbon    atoms   as  joined 

CH2 

by  a  double  bond;  we  should  expect  this  molecule  to  be 
very  unready  to  form  an  additive  compound.  Moreover 
molecules  supposed  to  contain  'free  bonds'  are  sometimes 
very  easily  produced  from  others  containing  only  'satisfied 
bonds';  e.g.  NO  is  formed  by  the  action  of  water  on 

1  This  reaction  is  usually  represented  thus  : 

C1=         C1-C  =  0 


Cl. 
M.  C. 


130  CHEMICAL  STATICS.  [§62 

N2O3  or  N2O4  [-N  =  O,  from  O  =  N-O-N  =  O  or 
O  =  N  — O  — O  — N  =  O]:  this  reaction  appears  to  be  op- 
posed to  all  ideas,  however  vague,  which  can  be  associated 
with  the  phrase  '  free  bonds.'  But  some  chemists  say  that 
'  a  double  bond '  is  the  same  thing  as  '  two  free  bonds ' :  very 
probably  they  are  right ;  one  does  not  venture  much  in 
asserting  identity  between  two  undefined  and  undefmable 
propositions. 

We  appear  then  to  gain  nothing  by  saying  that  an 
unsaturated  molecule  is  one  containing  free  bonds,  unless 
indeed  knowledge  is  advanced  by  explaining  the  unknown 
in  terms  of  the  unknowable1. 

62.  Lessen  attempts  to  attach  precise  meanings  to  the 
expressions  '  saturated '  and  ( unsaturated '  molecules.  A 
saturated  molecule,  he  defines  to  be,  one  in  which  each  poly- 
valent atom  directly  acts  on,  and  is  acted  on  by,  its  maximum 
number  of  monovalent  atoms  (see  formula,  p.  139,  par.  70). 
An  unsaturated  molecule,  he  defines  to  be,  a  molecule  in 
which  one,  or  more,  polyvalent  atom  acts  directly  on,  and  is 
acted  on  by,  less  than  its  maximum  number  of  monovalent 
atoms.  Saturated  molecules,  as  thus  defined,  can  combine 
only  with  polyvalent  atoms,  such  combination  being  pre- 
ceded by  rearrangement  of  the  mutual  direct  atomic  actions  : 
unsaturated  molecules  are  able  to  combine  directly  with  mo- 
novalent atoms.  As  an  example  of  an  unsaturated  molecule, 
we  may  take  the  compound  C2H4.  Granting  that  the  carbon 
atom  is  tetravalent,  it  follows  that  the  molecule  C2H4  is 
unsaturated,  because,  whether  we  suppose  the  mutual  atomic 
actions  to  be  represented  by  the  formula 

H 

H\  ^  I 

/C  — C  or  by         H  — C  — C  — H, 

IT  XH  1 

H 

1  Lessen  points  out  that  molecules  described  as  'containing  free  bonds'  can 
usually  take  part  in  reactions  wherein  condensation  of  volume  occurs,  e.g. 
CO  +  C12  =  COC12,   2CO  +  O2  =  2CO2,    2NO  +  O2  =  N2O4  (or  at  higher  tempera- 
tures 2NO  +  O2=2NO2),  4NO  +  O2=2N2O3,  &c.     [See  also  appendix  to  Section 
4  of  this  chapter.] 


§63]  ATOMIC   AND   MOLECULAR   SYSTEMS.  1  3  I: 

at  least  one  carbon  atom  is  directly  combined  with  less  than  its 
maximum  number  of  monovalent  atoms.  C2H4  can  combine 
with  monovalent  atoms,  e.g.  it  forms  C2H4Br2.  The  compound 
C2H6  affords  an  example  of  a  saturated  molecule.  As  the  valency 
of  the  carbon  atom  is  four,  C2H6  is  necessarily  saturated,  be- 
cause, however  the  interatomic  actions  are  represented  in  a 
formula,  each  carbon  atom  must  be  regarded  as  combined 
with  its  maximum  number  of  monovalent  atoms.  The  mole- 
cule C2H6O  can  be  produced  from  C2H6,  but  the  reactions 
which  occur  in  this  change,  and  also  the  properties  of  C2H6O, 
shew  that  the  interatomic  actions  are  differently  arranged  in 
the  two  molecules  C2H6  and  C2H6Ql. 

63.  It  is  evident  that  the  valency  of  only  a  minority  of 
the  elementary  atoms  can  be  considered  as  fairly  well  esta- 
blished. In  order  to  determine  the  valency  of  an  elementary 
atom  we  ought  to  have  several  gasifiable  compounds  of  that 
element  with  elements  whose  atoms  are  monovalent,  the 
molecules  of  such  compounds  containing  not  more  than  one 
atom  of  the  given  element2.  When  we  know  of  but  one 
such  compound  we  are  unable  to  fix  the  valency;  we  may 
however  say  that  the  valency  of  the  atom  is  probably  an  odd 
or  an  even  number  according  as  its  valency  in  the  given 

1  The  possible  formulae  are,  — 

H    H  H    H  H          H 

ii  II  ii 

H-C-C-H,  and  H-C-C-O-H  or  H-C-O-C-H 

ii  it  ii 

H    H  H    H  H          H 

respectively. 

2  Thus  the  valency  of  Al  cannot  be  determined  from  the  molecule  A12C16. 
The  formula  A^Clg  might  be  written 

Cl  Cl  Cl 

CK  /Cl       CL  \  <C\        C1\l  CL     |  /Cl 

Cl—  Al—  Al—  Cl,         ^Al—  Al^      ,      C1-A1—  Al,     or        XA1—  Al, 


Cl/  \C1      C\'/  Cl        r\/\        I  r\      I 

Cl  Cl     Cl  Cl 

the  valency  of  the  aluminium  atom  varying  from  i  to  7.  The  first  of  these  is  most 
probably  correct,  considering  the  general  properties  of  the  molecule  A12C16,  but 
the  evidence  is  not  sufficient  to  decide  that  Al  belongs  to  the  group  of  tetra- 
valent  atoms. 

9—2 


132  CHEMICAL  STATICS.  [§63 

molecule  is  an  odd  or  even  number1 ;  and  we  may  also  con- 
clude that  the  number  which  expresses  the  valency  of  the 
given  atom  in  the  special  molecule  under  consideration  will 
also  express  its  valency  in  many  other  molecules.  Although 
the  valency  of  an  atom  has  been  determined  from  a  con- 
sideration of  several  molecules  containing  that  atom,  it  is  still 
possible  that  this  number  does  not  express  the  true  valency ; 
but  until  the  number  is  proved  to  be  too  small  it  must  be 
used  as  the  true  valency  in  all  questions  regarding  structural 
formulae  of  molecules  containing  the  given  atom2. 

When  no  molecule  containing  monovalent  atoms,  com- 
bined with  a  single  atom — or  even  with  more  than  one 
atom— of  a  given  element  can  be  obtained,  any  number 
assigned  as  the  valency  of  the  atom  of  that  element  must  be 
very  doubtful. 

Many  non-gasifiable  compounds  containing  monovalent 
atoms  combined  with  atoms  of  a  single  other  element  are 
known  (e.g.  many  metallic  haloid  compounds) :  if  the  mole- 
cular weights  deduced  for  these  compounds  by  the  aid  of 
considerations  such  as  those  sketched  on  pp.  74 — 77  are 
assumed  to  be  the  true  relative  weights  of  the  molecules  of 
these  solid  compounds,  and  if  those  generalisations  which  have 
been  made  concerning  the  arrangement  of  atoms  in  gaseous 
molecules  are  assumed  to  hold  good  for  the  molecules  of 
solids  also,  then  the  valency  of  many  elementary  atoms 
not  included  in  the  table  on'  p.  121  could  be  determined. 
Thus,  if  we  assume  that  the  general  formula  MX  represents 
the  atomic  structure  of  the  molecules  of  the  solid  haloid 
salts  of  the  alkali  metals  (M  =  K,  Na,  Li,  &c.  and  X  =  F, 
Cl,  Br,  or  I)  then  the  atoms  of  these  metals  are  most 
probably  monovalent.  Most  of  the  generally  accepted  for- 
mulae for  salts  of  alkali  metals  may  be  written  with  the 
atoms  of  these  metals  represented  as  each  in  direct  com- 

1  When  'valency  of  an  atom'  is  spoken  of  without  mention  of  the  valency  in 
a  particular  molecule,  the  expression  is  always  to  be  understood  as  defined  on 
p.  122,  see  also  p.  127. 

2  If  this  rule  is  not  attended  to  endless  confusion  arises,  and  the  whole  theory 
of  valency  becomes  merely  an  amusing  exercise  of  fancy. 


§§63,64]       ATOMIC  AND   MOLECULAR   SYSTEMS.  133 

bination  with  only  one  other  atom,  but  whenever  this 
arrangement  has  become  somewhat  unsatisfactory  chemists 
have  not  hesitated  to  assume  that  the  atoms  of  the  alkali 
metals  may  be  tri-  penta-  or  even  heptavalent,  i.e.  may  each 
act  on,  and  be  acted  on  by,  3,  5,  or  7  other  atoms.  So  with 
other  elements  ;  from  a  consideration  of  solid  or  liquid  com- 
pounds only  no  trustworthy  conclusions  as  to  the  valencies  of 
the  atoms  in  the  molecules  of  these  compounds  can  be  deduced. 
It  is  so  easy,  after  making  the  two  fundamental  assumptions 
stated  above,  to  make  an  indefinite  number  of  further  assump- 
tions ;  it  becomes  so  pleasant  to  manipulate  formulae  on 
paper,  that  it  is  certainly  better — in  the  present  state  of 
knowledge — to  apply  the  theory  of  valency  only  to  gaseous 
molecules.  It  is  very  probable  that  the  valency  of  the 
elementary  atoms  varies  periodically  with  variations  in  the 
relative  weights  of  these  atoms :  if  this  general  statement  is 
thoroughly  established,  the  exact  nature  of  the  periodic 
function  is  determined,  and  the  true  atomic  weights  of  all  the 
elements  are  fixed,  we  shall  have  in  the  Periodic  Law  a  most 
important  method  for  determining  valencies.  But  a  great 
deal  of  work  must  be  done  before  this  '  law '  can  be  applied 
otherwise  than  generally  and  tentatively  to  questions  of 
valency  (see  chap.  III.  par.  115). 

SECTION  IV.    Allotropy  and  Isomerism. 

64.  Having  gained  the  conception  of  a  molecule  as  com- 
posed of  atoms,  each  directly  acting  on,  and  being  acted  on 
by,  a  definite  number  of  other  atoms,  we  at  once  regard  the 
molecule  as  a  structure ;  we  recognise  what  Frankland  in 
1852  happily  called  'limited  molecular  mobility.'  A  structure 
involves  arrangement  of  parts,  subordination  of  less  to  more 
important  parts;  it  supposes  the  existence  of  definite  actions 
for  fulfilling  which  the  structure  is  adapted ;  in  a  word, 
structure  means  correlation  of  properties  and  material  con- 
figuration1. 

1  When  '  arrangement  of  atoms  in  the  molecule '  is  spoken  of,  or  when  a 
similar  phrase  is  used,  it  is  to  be  taken  as  implying  only  a  rough  approximation 


134  CHEMICAL   STATICS.  [§§  65,  66 

And  when  we  consider  the  properties  of  individual  mole- 
cules the  justness  of  thus  regarding  each  as  a  definite  atomic 
structure  becomes  more  apparent.  We  find  many  compound 
molecules  containing  the  same  number  of  the  same  elementary 
atoms  yet  exhibiting  markedly  different  chemical  and  physical 
properties,  i.e.  we  find  the  phenomenon  of  Isomerism :  how  can 
we  account  for  this  except  by  assuming  (i)  that  each  mole- 
cule has  a  definite  atomic  structure,  and  (2)  that  the  same 
atoms  may  be  differently  arranged  in  different  molecules  ? 

65.  A  knowledge  of  the  atomic  configurations  of  series 
of  molecules,   supposing   this   to  be   gained,  must   be   sup- 
plemented by  a  knowledge  of  the  way  in  which  the  energy  of 
each  molecule  varies  with  variations  in  the  configuration  and 
motion  of  its  constituent  atoms,  before  a  complete  knowledge 
of  the  dynamical  properties  of  these  molecules  is  possible. 
But  chemistry  is  yet  far  from  this  goal ;  she  is  obliged  to  be 
content  with  a  very  partial  and  sometimes  very  vague  know- 
ledge concerning  the  relative  atomic  configurations  of  a  few 
molecules ;  she  has  hardly  entered  on  the  second  part  of  her 
task. 

66.  Granting   then    that    variations    in    the   properties 
(chemical  and  physical)  of  molecules  accompany  variations 
in  the  atomic  configurations  of  these  molecules,  it  is  con- 
ceivable that  the  latter  variations  may  consist  of 

(1)  variations  in  the  relative  positions  of  the  atoms, 

(2)  variations  in  the  distances  between  the  atoms,  their 

relative  positions  being  constant. 

To  illustrate  this  point,  let  us  take  the  molecule  C2HGO. 
More  than  one  compound  exists  the  molecules  of  which 
have  the  atomic  composition  expressed  by  this  formula.  On 
the  first  assumption,  viz.  that  variation  of  properties  is  to  be 
correlated  with  variations  in  the  relative  positions  of  the 

to  a  knowledge  of  atomic  arrangements.  Structural  formulae  sum  up  facts  of 
formation  and  decomposition,  and,  assuming  the  fundamental  positions  of  the 
molecular  theory,  exhibit,  in  a  rough  and  general  way,  connections  between  these 
facts  and  the  directions  of  the  mutual  actions  of  the  atoms  in  the  molecules  of  the 
compounds  formulated.  No  attempt  is  made  in  these  formulae  to  express  quanti- 
tative measurements  of  atomic  interactions. 

' 


§66]  ATOMIC  AND   MOLECULAR   SYSTEMS.  135 

atoms  in  the  molecule,  we  find  that  there  are  two  possible 
arrangements  of  the  two  carbon,  six  hydrogen,  and  one  oxy- 
gen atoms  (assuming  the  valency  of  the  carbon,  hydrogen, 
and  oxygen  atom  to  be  4,  i,  and  2  respectively),  viz. 

(rt)  H     H  (ff)  H  H 

I  I 

H  —  C  — C  —  O  —  H,  H  — C  — O  — C  — H; 

II  II 

H      H  H  H 

hence,  two  compounds,  each  having  the  composition  ex- 
pressed by  the  empirical  formula  C2H6O,  may  exist. 

But  if  we  make  the  second  assumption,  viz.  that  variation 
of  properties  is  to  be  correlated  with  variations  in  the  dis- 
tances between  the  atoms  in  the  molecule,  the  relative  posi- 
tions of  these  atoms  remaining  unchanged,  we  may  have 
an  apparently  unlimited  number  of  compounds  of  the  for- 
mula C2H6O ;  such  compounds  might  perhaps  be  repre- 
sented in  this  way, — 

(a)         H     H  (b)  H     H 

II  II 

H  — C  — C  — O  — H,  H C  — C O  — H, 

I        I  I 

H     H 

H     H 

(c)  H  H 


H  — C C  — O  — H, 

I  I 

H  H 

and  so  on. 

Now  as  only  two  compounds,  C2H6O,  are  know  to  exist, 
we  have  a  presumption  in  favour  of  the  first  supposition : 
much  stress  cannot  however  be  laid  on  this  argument.  More- 
over if  the  second  of  the  two  suppositions  is  correct,  then  any 
molecule  containing  two  atoms  should  be  capable  of  existing 
in  more  than  one  modification  ;  in  other  words,  every  di- 
atomic molecule  should  be  capable  of  shewing  isomerism. 
But  there  is  no  certainly-established  instance  of  isomerism 
exhibited  by  any  molecule  containing  less  than  three  atoms; 


136  CHEMICAL   STATICS.  [§67 

therefore,  as  the  assumption  that  variations  of  properties 
exhibited  by  compounds  having  the  same  composition  and 
same  molecular  weight  are  connected  with  variations  in 
the  relative  positions  of  the  atoms  composing  the  molecules 
of  these  compounds,  suffices  to  explain  the  vast  majority  of 
well-authenticated  cases  of  isomerism  among  gaseous  mole- 
cules, we  conclude  that  it  is  better,  at  any  rate  at  present, 
to  build  the  general  theory  of  isomerism  on  this  hypo- 
thesis1. 

67.  But  before  more  fully  considering  this  subject,  it  will 
be  well  to  glance  at  the  allied  phenomena  of  allotropy  and 
polymerism. 

The  table  on  p.  42  shews  that  of  the  thirteen  elements 
whose  molecular  weights  have  been  determined  by  the  help 
of  Avogadro's  law,  four,  viz,  oxygen,  sulphur,  selenion  and 
iodine  (probably  bromine  also)  possess  a  smaller  molecular 
weight  at  high  than  at  lower  temperatures ; — the.  number  of 
atoms  in  the  molecule  of  oxygen  at  temperatures  below 
about  300°,  and  under  special  conditions  is  3,  at  tem- 
peratures above  300°  it  is  2 ;  the  molecule  of  sulphur  at 
temperatures  not  much  higher  than  the  boiling  point  of  that 
element  contains  6  atoms,  and  at  somewhat  higher  tem- 
peratures 2  atoms  ;  the  number  of  atoms  in  the  molecule 
of  selenion  varies  from  3  to  2,  and  in,  the  molecule  of  iodine 
(and  probably  also  in  that  of  bromine)  from  2  to  I,  according 
to  temperature.  We  know  that  the  properties  correlated 
with  the  existence  of  the  triatomic  molecule  O3  differ  much 
from  those  which  characterise  the  diatomic  molecule  O2:  no 
experiments  have  been  made  to  compare  the  properties  of 
the  hexatomic  with  those  of  the  diatomic  molecules  of 
sulphur,  of  the  triatomic  with  the  diatomic  molecules  of 
selenion,  and  of  the  diatomic  with  the  monatomic  molecules 
of  iodine. 

Of  the   15  or   16  nonmetallic  elements,  phosphorus  and 

1  The  supposition  that  isomerism  may  be  due  to  variations  in  the  distanct 
between  atoms,  the  relative  positions  of  which  remain  unchanged,  appears  to 
opposed    to   the    results  of  physical  experiments  which  are  in   agreement   witl 
deductions  made  from  the  kinetic  theory  of  gases.     See  Lessen,  loc.  cit.  p.  269. 


§6;]  ATOMIC  AND   MOLECULAR   SYSTEMS.  137 

arsenic,  boron,  carbon  and  silicon — besides  sulphur  and  sele- 
nion — exhibit  marked  variations  in  physical  and  chemical 
properties  when  in  the  solid  state.  We  certainly  are  not 
justified  in  unconditionally  asserting  that  these  variations 
of  properties  accompany  differences  in  the  atomic  configura- 
tions of  the  molecules,  or  differences  in  the  numbers  of  atoms 
in  the  molecules,  of  red  and  yellow  phosphorus,  or  of  octahe- 
dral and  prismatic  sulphur,  &c.  When  the  differences  in 
properties  are  chiefly  physical  (e.g.  differences  in  crystalline 
form,  in  specific  gravity,  in  melting  points,  &c.),  they  may 
very  probably  be  correlated  with  differences  in  the  molecular, 
rather  than  in  the  atomic,  configurations  of  the  various  modi- 
fications of  the  element  in  question1. 

Be  this  however  as  it  may,  the  differences  experimentally 
shewn  to  exist  between  the  properties  of  the  molecules  of 
gaseous  oxygen  and  ozone  are  explicable  in  terms  of  the 
molecular  theory  only  by  admitting  that  the  properties  of 
a  molecule  are  dependent  not  only  on  the  nature  but  also 
on  the  number  of  the  atoms  which  compose  it2. 

The  marked  chemical  differences  between  red  and  yellow 
phosphorus  would  lead  us  to  expect  that  the  molecular 
weight  of  gaseous  phosphorus  would  be  found  to  vary  with 
variations  of  temperature  :  such  variations  have  not  however 
as  yet  been  observed3. 


1  See  section  5.  of  present  chapter. 

2  It  ought  to  be  noted  that  change  from  one  allotropic  form  to  another,  is 
accompanied  by  evolution  or  absorption  of  heat;   see  post,  chap.  IV.,  par.  125. 

3  V.  Meyer  states  \Ber.  14.  1455 ;   see  also  do.  13.  1116  note]  that  the  vapour 
densities  of  phosphorus  and  arsenic  at  very  high  temperatures  point  to  the  ex- 
istence of  molecules  weighing  less  than  P4  and  As4  respectively. 

There  are  some  interesting  observations  bearing  on  the  subject  of  allotropy  by 
W.  Spring  in  the  Berichte  [see  especially  16.  1002 — 3],  Spring  finds  that  when  an 
element  which  exhibits  allotropy  is  subjected  to  great  pressure,  that  modification 
which  has  the  greatest  specific  gravity  is  produced.  Yellow  phosphorus  is  changed 
into  red  by  compression  :  red  phosphorus  and  sulphur  do  not  combine  until  heated 
to  260°,  i.e.  to  the  temperature  at  which  red  is  changed  to  yellow  phosphorus;  red 
phosphorus  does  not  combine  with  sulphur  when  the  two  are  subjected  to  a  pres- 
sure of  6500  atmospheres,  at  which  pressure  many  metallic  sulphides  are  pro- 
duced. Hence  Spring  concludes  that  red  phosphorus  is  less  chemically  energetic 
than  yellow;  and  generally  that  the  more  a  solid  substance  is  rendered  dense,  the 


138  CHEMICAL  STATICS.  [§§68,69 

68.  The  names  allotropy  and  polymerism  are  applied  to 
analogous  phenomena  exhibited  by  elements  and  compounds 
respectively. 

If  two  molecules  exist,  consisting  of  the  same  elementary 
atoms,  but  one  heavier  than  the  other,  the  heavier  molecule  is 
said  to  be  a  'polymeric  modification/  or  a  'polymeride'  of  the 
other: — thus  C10H20  is  a  polymeride  of  C5H10,  C^H^  is  a 
polymeride  of  C10H16,  H3C3N3O3  is  a  polymeride  of  HCNO, 
C6H12O3  is  a  polymeride  of  C2H4O.  Glucose,  ;trC6H12O6,  is 
not  however  regarded  as  a  polymeride  of  ethylene  oxide, 
C2H4O:  the  name  is  restricted  to  those  molecules  whose 
weight  is  a  multiple  of  that  of  other  molecules,  and  which 
are  obtained  by  simple  reactions,  generally  by  the  action  of 
heat,  from  these  other  molecules.  Thus,  ethaldehyde,  C2H4O, 
is  easily  polymerised,  e.g.  by  the  action  of  a  very  little  hydro- 
chloric or  sulphuric  acid,  with  formation  of  parethaldehyde, 
C6H12O3 ;  but  the  latter  body  is  not  directly  obtainable  from 
ethylene  oxide,  although  the  molecule  of  this  compound,  like 
that  of  ethaldehyde,  contains  2  atoms  of  carbon,  4  of  hydro- 
gen, and  I  of  oxygen. 

But  few  examples  of  undoubted  polymerism  are  fur- 
nished by  compounds  of  the  elements  other  than  carbon ; 
one  of  the  most  marked  cases  is  the  molecule  N2O4,  which 
is  a  polymeride  of  NO2,  another  is  furnished  by  the  mole- 
cules Sn2Cl4  and  SnCl2. 

69.  The  phenomena  summarised  in  the  term  isomerism, 
i.e.  the  existence  of  molecules  characterised  by  different  pro- 
perties but  containing  the  same  number  of  the  same  atoms, 
must  now  be  examined  in  some  detail. 

Isomeric  compounds  are  generally  said  to  be  *  metameric ' 
when  they  belong  to  different  chemical  types.  This  state- 
ment does  not  of  course  furnish  a  definition  of  metameric 
compounds ;  but  it  is  sufficient.  Various  hydrocarbons,  all 
possessed  of  the  general  properties  of  paraffins,  but  each 
differing  in  some  properties — chemical  and  physical — from  the 
others,  are  represented  by  the  formula  CGHU :  various  hydro- 
more  is  its  chemical  activity  decreased.  Red  phosphorus  he  regards  as  ^. 
of  yellow  phosphorus. 


§  70]  ATOMIC  AND   MOLECULAR  SYSTEMS.  139 

carbons,  all  benzenes,  but  each  characterised  by  its  own  special 
properties,  are  represented  by  the  formula  C8H10:  the  different 
paraffins — C6H14,  or  the  different  benzenes,  C8H10 — are  said  to 
be  isomerides  one  of  the  other.  But  although  two  molecules 
are  represented  by  the  formula  C2H6O,  yet  these  belong  to 
very  different  types,  or  groups  of  compounds ;  one  is  a  pri- 
mary alcohol,  the  other  an  ether :  so  again  allylic  alcohol  and 
dimethyl  ketone  have  both  the  formula  C3H6O,  but  these 
bodies  are  altogether  distinct  in  their  chemical  properties — 
such  compounds  are  said  to  be  metameric.  Metamerides 
are  thus  seen  to  be  a  sub-class  included  in  the  larger  class  of 
isomeric  compounds. 

A  few  inorganic  compounds  exhibit  phenomena  which 
may  be  explained  by  supposing  the  existence  of  isomeric 
molecules,  but  it  is  only  when  we  study  the  compounds 
of  carbon  that  we  are  obliged  to  admit  that  molecules  may 
contain  the  same  numbers  of  the  same  atoms  but  differ  in 
chemical  and  physical  properties. 

70.  The  theory  of  valency  having  led  to  the  recognition 
of  the  molecule  as  a  structure,  may  be  carried  further ;  it 
may  guide  us  in  determining  the  probable  relative  structures 
of  isomeric  molecules  (see  note  to  p.  133). 

If  it  be  granted  that  isomerism  is  correlated  with  different 
relative  positions  of  atoms,  but  not  with  different  distances 
between  atoms  in  the  same  relative  positions  in  the  molecule1, 
(see  p.  134),  it  follows,  that,  a  molecule  containing  not  more 
than  two  atoms  cannot  exhibit  isomerism.  The  maximum 
number  of  monovalent  atoms  which  can  be  combined  with 
polyvalent  atoms  in  a  molecule  is  found  by  the  formula2 

«!  =  «3  +  2nA  +  3«5  +  4«6  +  2> 

where  n^  ti3,  ;/4,  &c.  represent  the  numbers  of  monovalent, 
trivalent,  tetravalent,  &c.  atoms  in  the  molecule.  Any  mole- 
cule in  which  the  value  of  nl  agrees  with  that  deduced  from 

1  Such  formulae  as  O  =  N-  and  =N-O-  are  really,  at  present,  the  same. 

2  See  Lothar  Meyer,  Die  Moderncn  Theorien  der  Chemie  (.fin  Ed.),  pp.  218 
ct  secj.,  of  which  pages  free  use  has  been  made  in  these  paragraphs. 


140  CHEMICAL  STATICS.  [§  71 

this  formula  must  necessarily  be  a  saturated  molecule1.  But 
each  polyvalent  atom  in  a  molecule  does  not  necessarily  act 
on  the  maximum  number  of  other  atoms;  in  many  molecules 


when  this  holds  good,  some  polyvalent  atoms  must  have 
within  their  '  binding  spheres'  less  than  the  maximum  number 
of  atoms,  in  other  words,  some  atoms  usually  divalent  must, 
in  this  molecule,  be  monovalent,  or  some  usually  trivalent 
must,  in  this  molecule,  be  divalent  &c.  This  is  expressed  in 
ordinary  nomenclature  by  saying  that  some  of  the  polyva- 
lent atoms  must  be  linked  by  'double'  or  'treble  bonds',  or 
that  some  of  the  '  bonds'  (sometimes  it  is  said,  of  the  '  affini- 
ties') of  the  polyvalent  atoms  must  be  'mutually  satisfied.' 
But  I  have  tried  to  shew  that  these  expressions  are  delusive, 
and  that  Lossen's  method  of  regarding  valency  is  preferable 
to  any  yet  proposed. 

71.  The  number  of  ways  in  which  the  atoms  com- 
prising a  complex  molecule  may  be  arranged  is  evidently 
very  great2:  to  determine  the  maximum  number  of  possible 
isomerides  of  a  given  formula  is  a  purely  mathematical 
problem.  At  present  we  seem  justified  in  concluding  that 
many  atomic  configurations  which  are  mathematically  pos- 
sible, are  physically  impossible  ;  this  is  equivalent  to  saying 
that  the  stability  of  molecules  does  not  depend  solely  on 
the  valencies  of  their  constituent  atoms.  To  determine 
which  of  the  possible  configurations  of  a  given  number  of 
atoms  are  stable  ;  to  generalise  the  connections  undoubtedly 
existing  between  molecular  structure  and  stability,  and  also 
between  this  structure  and  the  functions  of  the  molecule  or 
of  parts  thereof;  this  is  the  task  that  chemists  are  now 
elaborating. 

1  See  definition  on  p.  130. 

2  Thus,  Prof.  Cayley,  Brit.  Ass.  Reports  for  1875,  P-  257>  giyes  the  following 
statement,  exhibiting  the  relations  between  the  number  of  carbon  atoms  in  the 
molecules  of  paraffins  and  the  number  of  isomeric  modifications  of  each  molecule 
allowed  by  the  theory  of  valency. 

Number  of  carbon  atoms  in  molecule  of  paraffin,  i.   4.   7.    10.     12.     13. 
Number  of  possible  isomerides          ...          ...         i.   2.   9.   75.   357.   799. 


§§  72>  73]         ATOMIC   AND   MOLECULAR  SYSTEMS.  141 

72.  The  molecular  formula  of  a  compound  alone  some- 
times  gives    us   a   considerable  amount    of   information    re- 
garding the  structure  of  the    molecule    of  that    compound. 
Thus  we  appear  justified,  at  present,  in  making  the  following 
assertions;  (i)  molecules  containing  only  monovalent  atoms 
cannot  exhibit  isomerism  ;  (2)  molecules  containing  a  single 
polyvalent  atom  united  with  monovalent  atoms  only  cannot 
exhibit   isomerism  ;    (3)   isomerism  cannot  be  exhibited  by 
molecules  containing  two  polyvalent  atoms  united  with  mono- 
valent atoms,  provided  the  latter  are  all  atoms  of  the  same 
element,  or  all  but  one  atoms  of  the  same  element,  when  the 
two  polyvalent   atoms   are   themselves   atoms   of  the   same 
element. 

73.  Any   molecule   containing   more    than    two   atoms 
and  not  belonging  to  one  of  the  classes  above  defined,  may 
exhibit  isomerism.     The  possible  variations  of  structure  even 
in  molecules  containing  a  small  number  of  atoms  may  be 
large.     Thus  N2O  may  have  the  structure 

(i)     N  —  N,  or  the  structure  (2)     N  — N  —  O, 

^o^ 

(neither  the  nitrogen  nor  the  oxygen  atoms  can  act  on  more 
than  two  atoms,  i.e.  neither  can  be  more  than  divalent1). 
NO  can  be  regarded  only  as  N  —  O.  NO2  may  be 

(:)  O  — N  — O,    or    (2)  O  — N  — O,     or    (s)N  —  O  —  O. 

N2O4  may  have  many  structures,  e.g. 

(!)  o- N  — N  — O,        or        (2)  O  — N  — N  — O, 

I      I  xox      xox 

o     o 

or    (3)  N  — O  — O  — N,        or        (4)  N  — O  — O  — N, 
I                         I                             I  I 

O  O  O O 

or    (5)  N  — O  — O  — O— O  — N,    or    (6)  N  —  N— O  —  O  —  O  —  O,  &c. 
In  the  case  of  N2O,  the  first  of  the  possible  structures 

1  Lossen's  nomenclature  and  notation  are  used  here  and  generally  throughout 
the  rest  of  this  book. 


142  CHEMICAL   STATICS.  [§  73 

better  represents  the  arrangement  of  atoms  in  this  molecule 
than  the  other,  inasmuch  as  the  reactions  of  this  compound 
shew  that  there  is  no  difference  in  the  functions  of  the  two 
nitrogen  atoms  in  the  molecule ;  for  a  similar  reason  the 
third  formula  for  NO2  and  the  sixth  for  N2O4  are  inadmis- 
sible; the  fifth  formula  for  N2O4  is  improbable  because,  among 
other  reasons,  it  would  lead  to  N  —  O  —  O  as  the  formula  for 
NO2;  the  fourth  formula  for  N2O4  would  lead  us  to  expect 
that  this  compound  when  heated  would  decompose  into  NO 
and  O2,  but  we  know  that  it  gives  2NO2.  Formulae  (i)  and 
(2)  very  simply  express  the  formation  of  N2O4  by  cooling 
2NO2,  and  the  formation  of  2NO2  by  heating  N2O4,  and 
therefore^  the,  structure  of  the  molecule  N2O4  is  more  prob- 
ably expressed  by  one  or  other  of  these  formulae  than  by 
any  other  of  the  six  given  above. 

The  compounds  of  carbon  present  the  best  field  for  the 
study  of  isomerism. 

It  has  been  already  stated  that  a  molecule  containing 
two  carbon  (tetravalent)  atoms  united  with  five  monovalent 
atoms  of  one  element  and  one  monovalent  atom  of  another 
element,  (i.e.  a  molecule  of  the  form  C2X3X')  cannot  exhibit 
isomerism.  If  however  there  are  four  monad  atoms  of  one 
kind,  and  two  of  another  in  the  molecule  (if  the  form  of  the 
molecule  is  .represented  by  the  symbol  C2X4X/2)  isomerism 
becomes  possible ;  thus  C2H4C12  may  have  the  structure 

H     H  H     H 

II  II 

Cl  — C  — C  — Cl,  or         H  — C  — C  — Cl 

II  II 

H     H  H     Cl 

/or  more  shortly,  CH2Cland  CH3    \.    But  when  three  carbon 

I'll 

CH2C1        CHC12/ 

atoms  combine  with  monovalent  atoms,  the  existence  in  the 
molecule  thus  produced  of  a  single  monad  atom  of  an  element 
different  from  that  forming  the  other  monad  atoms  renders 
isomerism  possible ;  thus  C3H7C1  (which  belongs  to  the 
general  form  C3X7X')  may  have  the  structure 


§  73]  ATOMIC  AND   MOLECULAR   SYSTEMS.  143 

CH3  CH3 

CH2  or  CHC1  : 

I  1 

CH2C1  CH3 

So  also  four  molecules  C3HfiCl2,  five  molecules  C3H5C13,  six 
CgH^CLt1,  five  C3H3C15,  &c.  may  exist.  Molecules  containing 
four,  or  more  than  four  atoms  of  carbon  combined  with 
monovalent  atoms  may  exhibit  isomerism  even  when  all  the 
monad  atoms  are  of  one  kind,  (i.e.  molecules  of  the  general 
form  C4X10):  thus  C4H10  may  have  the  structure 

f  • 

CH2  or 

CH2 

I 
CH3 

Molecules  containing  five  carbon  atoms  may  have  thel 
arranged  in  three  ways,  as  represented  by  the  formulae 

C 
I 
C  — C  — C  — C  — C,     C  — C  — C  — C,     and    C  — C  — C. 


When  six  carbon  atoms  are  present  in  the  molecule  these 
atoms  may  be  arranged  in  five  ways,  viz. 

C  — C  — C  — C  — C  — C.     C  — C  — C  — C  — C,     C  — C  — C  — C  — C, 

I  I 

C  C 

c  • 

I 

c  — c  —  c— c,      c— c  — c  — c. 

I     I  I 

c    c  c 

When  eight  carbon  atoms  are  present,  they  may  be  arranged 

1  Viz.        CHoCl        CHCL        CC13        CHC12        CC13          CH3 
I  I  I  I  I  I 

CC12  CH2  CHC1      CHC1         CH2          CC12 

!  Ill  II 

CH2C1        CHC12        CH3        CH2C1        CH2C1      CHC12. 


144  CHEMICAL   STATICS.  [§  73 

in  1  8  different  ways,  &c.  The  maximum  number  of  mono- 
valent  atoms  which  can  be  combined  with  any  of  these 
arrangements  of  carbon  atoms  is  found  by  the  formula 
/21  =  2;z4+2  where  ;z4  =  number  of  carbon  atoms1.  But  all 
the  carbon  atoms  in  a  molecule  are  not  necessarily  tetrava- 
lent  in  that  molecule  (in  the  ordinary  nomenclature  some  of 
the  carbon  atoms  may  be  doubly  or  trebly  linked  to  one 
another,  or  there  may  exist  'free  affinities').  Now  the  gene- 
ral formula  given  on  p.  139,  viz. 


shews  that  the  maximum  number  of  monad  atoms  in  such 
a  molecule  is  dependent  only  on  the  number  of  trivalent 
and  tetravalent,  and  is  independent  of  the  number  of  diva- 
lent, carbon  atoms  in  the  molecule.  But  in  applying  this 
formula  it  is  assumed  that  the  number  of  carbon  atoms 
which  are  actually  trivalent,  and  of  those  which  are  actually 
tetravalent  in  any  given  molecule,  can  be  determined.  It 
is  better  to  represent  the  molecule  of  a  carbon  compound,  if 
possible,  as  containing  only  tetravalent  carbon  atoms  :  in 
many  cases  however  this  cannot  be  done  ;  in  any  case  the 
reactions  of  the  compound  must  be  studied  before  a  formula 
is  given  to  it. 

Let  us  suppose  we  are  required  to  assign  formulae  to 
compound  molecules  containing  carbon,  hydrogen,  and  oxygen 
atoms.  When  the  equation  n±  —  2n±  +  2  is  satisfied,  the  struc- 
tural formula  assigned  to  the  molecule  must  evidently  con- 
tain only  tetravalent  carbon  atoms  ;  several  such  formulae 
may  however  be  possible,  —  thus  for  the  molecule  C3H8O,  two 
structural  formulae 

CH3  CH3 

CH2  and  CH2 

CH2  O 

I  I 

O  —  H  CH3 

1  See  Lothar  Meyer,  he.  cit.  pp.  240  —  242. 


§  73]  ATOMIC   AND   MOLECULAR   SYSTEMS.  145 

fulfil  the  conditions  required.  In  accordance  with  generalisa- 
tions which  have  been  made  correlating  structure  and  pro- 
perties, the  first  of  these  formulae  belongs  to  a  primary 
alcohol,  the  second  to  a  mixed  ether  :  two,  and  only  two 
compounds,  C3H8O,  are  known,  one  exhibiting  the  proper- 
ties of  a  primary  alcohol,  the  other  those  of  a  mixed  ether. 
When  however  n^  <  2/z4  +  2,  and  divalent  atoms  are  also  present 
in  the  molecule,  the  formula  may  contain  only  tetravalent 
carbon  atoms,  or  it  may  contain  tetravalent,  and  also  di- 
or  trivalent  carbon  atoms.  Thus  in  C3H6O  nl  =  2?z4 ;  two 
structural  formulae  are  possible  wherein  each  carbon  atom  is 
tetravalent,  viz. 

(i)       /CH2  (2)        CH3 

O     CH2  and  >CH. 

v  °0 

\CH2  CB2 

Each  of  these  is  the  formula  of .  an  ether;  in  propylene 
oxide  we  have  an  ether  the  properties  of  which  shew 
that  it  is  probably  described  by  the  first  of  these  formulae. 
Six  structural  formulae  are  possible  for  the  molecule 
C3H6O,  provided  some  of  the  carbon  atoms  may  be  tri-  or 
divalent.  Three  compounds  having  this  formula  (besides 
propylene  oxide)  are  known;  of  these,  one  is  a  ketone,  i.e. 
belongs  to  a  class  of  compounds  the  molecules  of  which  are 
generally  regarded  as  containing  a  carbon  and  an  oxygen 
atom  in  direct  union  ;  another  is  an  aldehyde,  i.e.  belongs  to 
a  class  of  compounds  the  molecules  of  which  are  regarded  as 
containing  a  carbon  atom  in  direct  combination  with  one 
oxygen  and  one  hydrogen  atom  ;  and  the  third  is  an  alcohol, 
probably  a  primary  alcohol.  The  six  possible  formulae  are 


(I) 

(2) 

(3) 

(4) 

(5) 

(6) 

CH3 

CH3 

CH2 

CH3 

CH3 

CH3 

1 

1 

1 

1 

1 

i 

c  —  o 

CH2 

CH 

CH2 

C 

CH. 

1 

1 

1 

1 

1 

I 

CH3 

H  —  C  —  O 

CH2 

C  —  O  —  H 

CH2 

CH 

| 

I 

1 

O  —  H 

O  —  H 

0  —  H 

M.  C.  10 


146  CHEMICAL   STATICS.  [§§  73,  74 

The  first  and  second  formulae  contain  each  one  trivalent  carbon 
atom,  and  the  oxygen  atom  is  monovalent  in  both,  the  third 
contains  one  trivalent,  the  fourth  and  fifth  each  one  divalent 
carbon  atom,  and  the  sixth  contains  two  trivalent  carbon  atoms. 
Formulae  (i)  and  (2)  are  appropriated  by  dimethyl  ketone  and 
propaldehyde  respectively ;  of  the  remaining  four,  (3)  and  (5) 
represent  allylic  alcohol  as  a  primary,  (6)  as  a  secondary,  and 
(4)  as  a  tertiary  alcohol.  Judging  from  the  general  reactions 
of  allylic  alcohol,  this  compound  is  probably  a  primary 
alcohol.  Formula  (3)  is  preferable  to  (5),  because  the  latter 
would  lead  us  to  expect  acetic  acid  /CH3  \  as  one  of  the 

\C02H/ 

products  of  oxidation  of  allylic  alcohol ;  inasmuch  as  acetic 
acid  is  not  produced  in  this  oxidation,  formula  (3)  more 
probably  expresses  the  structure  of  the  molecule  of  allylic 
alcohol  than  any  other  possible  formula. 

74.  In  these  examples  of  the  method  adopted  for  de- 
termining the  structural  formula  of  a  compound,  several 
generalisations  concerning  the  connection  of  structure  with 
properties  have  been  assumed  :  e.g.  that,  if  a  given  compound 
exhibits  aldehydic  properties,  the  structural  formula  of  the 
molecule  is  to  be  written  as  containing  the  atomic  group 
COH  ;  that  two  structures  are  possible  for  this  group,  one  in 
which  the  carbon  atom  acts  directly  on  the  oxygen  and  on 
the  hydrogen  atoms  (H  —  C  —  O),  the  other  in  which  direct 
action  occurs  only  between  the  carbon  and  the  oxygen  atoms 
(C  —  O  —  H)  ;  further,  the  first  of  these  structures  is  as- 
sumed to  be  correlated  with  the  group  of  properties  connoted 
by  the  word  '  aldehydic/  the  second  with  the  properties  con- 
noted by  the  expression  '  tertiary  alcoholic.'  When  therefore 
a  new  carbon  compound  is  discovered,  it  is  necessary  to 
determine,  as  far  as  possible,  to  what  group  of  compounds  it 
belongs ;  the  existence  of  a  certain  atomic  group  (or  groups) 
in  the  molecule  of  the  compound  may  then  generally  be 
predicated,  and  the  number  of  possible  structural  formulae 
may  thus  be  considerably  diminished.  But  the  classifica- 
tion of  the  carbon  compounds  is  certainly  not  yet  complete; 


§  74]  ATOMIC  AND   MOLECULAR   SYSTEMS.  147 

hence  arise  two  difficulties,  (i)  a  new  compound  may  belong 
to  a  class  no  other  member  of  which  has  been  previously 
examined,  in  which  case  no  class-group  can  be  assigned  to 
the  formula  of  the  new  compound  ;  or  (2)  a  compound  may 
be  prepared  whose  properties  indicate  that  it  belongs  to  one 
of  the  known  classes,  and  yet  the  group  which  generally 
marks  this  class  may  not  be  present  in  the  molecule  of  this 
particular  compound.  The  following  cases  may  be  taken  as 
illustrations  of  these  difficulties. 

(1)  It  was  known  that  the  action   of  nitrous   acid   on 
carbon  compounds  containing  the  group  NH2  (amido-deriva- 
tives)  resulted  in  the  production  of  compounds  differing  from 
the  original  by  containing  OH  in  place  of  NH2 ;  but  when 
nitrous  acid  acted  on  certain  amido-derivatives  of  benzene, 
compound    molecules    containing   one   nitrogen    atom    more 
and  two  hydrogen   atoms   less   than   the   original    molecule 
were    obtained.      The    reaction    appeared   to   be   abnormal. 
Several   of  the   new    compounds  were  prepared,  their   pro- 
perties were  studied,  and  the  existence  of  a  new  class   of 
carbon  compounds  was  recognised,  the  relations  of  which  to 
other  classes  appeared  to  be  best  summarised   in   formulae 
containing  the  characteristic  group  —  N2— . 

Certain  peculiar  and  definite  properties  appear  to  be 
always  associated  with  this  group  ;  it  has  recently  been  shewn 
that  the  formation  of  molecules  containing  this  group  and 
derived  from  compounds  of  the  '  fatty '  or  '  paraffinoid '  series 
is  possible  under  special  conditions. 

(2)  As  the  result  of  long   and   varied    experience,   the 
generalisation  has  been  made  that  the  molecules  of  carbon 
acids   contain    the   characteristic  group   H  —  O  —  C  —  O,  but 
from  time  to  time  compounds  have  been   prepared  exhibit- 
ing  acid  properties,  but  possessed  of  a  molecular   structure 
from  which  the  characteristic  group  is  absent.      Thus    C3H8 
yields  C3H7NO2,  and  from   this   compound    two    isomerides 
C3H6BrNO2  are  obtained,  one  of  which  is  a  monobasic  acid, 
while  the  other  does  not  shew  acid  properties ;  the  possible 
formulae  for  these  isomerides  are 

10 — 2 


148  CHEMICAL  STATICS^  [§  74 

NO2  H2     H 

I  I        I 

(i)     H3C  — C  — CH3,      and  (2)     H3C  — C  — C  — NO2; 

Br  Br 

from  a  consideration  of  the  general  properties  of  the  two 
isomerides  and  their  relations  to  other  compounds,  the  second 
formula  is  assigned  to  the  acid.  Hence  we  are  obliged  to 
conclude  that  although  most  known  carbon  acids  are  charac- 
terised by  the  atomic  group  H  —  O  —  C  —  O,  yet  a  substance 
may  be  a  true  acid  in  the  molecule  of  which  this  group  is  not 
present. 

A  very  instructive  example  of  the  difficulties  to  be  over- 
come before  a  general  structural  formula  can  be  assigned  to  a 
group  of  carbon  compounds,  is  afforded  by  the  investigations 
which  have  been,  and  are  being  made  into  the  constitution 
of  the  quinones1. 

These  examples  (and  others  might  easily  be  added)  shew 
how  undesirable  it  is  to  regard  the  present  system  of  classifi- 
cation of  carbon  compounds  as  final.  As  facts  are  accumu- 
lated, the  atomic  grouping  which  was  regarded  as  a  class- 
group  sometimes  becomes  the  group  of  a  larger  class, 
sub-classes  being  formed,  each  characterised  by  its  special 
group,  and  yet  each  containing  the  class-group.  Thus,  from 
the  analogy  between  metallic  hydroxides  and  alcohols,  and 
for  other  reasons,  the  group  O  —  H  was  assigned  to  alcohols 
(e.g.  C2H5.OH,  C3H7.OH,  &c.,  &c.)  ;  but  it  became  evident 
that  a  sub-division  of  this  great  group  was  required ;  facts 
were  amassed  and  formulae  devised  to  generalise  these  facts, 
until  most  chemists  are  now  agreed  that  the  molecules  of 
those  alcohols  called  '  primary '  (which  yield  certain  defi- 
nite products  when  oxidised,  &c.)  contain  the  atomic  group 
H  —  O  —  CH2,  the  molecules  of  those  called  '  secondary '  (and 
which  yield  other,  but  also  definite  products  when  oxidised) 
contain  the  group  H  -  O  —  C  -  H,  and  the  molecules  of  those 
called  'tertiary'  (which  yield  a  third  distinct  set  of  products 
when  oxidised)  contain  the  group  C  —  O  —  H. 

1  See  Armstrong  and  Groves,  loc.  cit.  pp.  812,  813. 


§  74]  ATOMIC   AND   MOLECULAR   SYSTEMS.  149 

Each  of  these  '  alcoholic  groups '  itself  contains  the 
group  O  -  H  ;  but  the  *  acid  group '  H  -  O  —  C  -  O  also 
contains  this  group ;  now  we  know  that  the  function  per- 
formed by  hydrogen  in  an  alcoholic  molecule  is  not  the  same 
as  that  performed  by  hydrogen  in  an  acid  molecule, — e.g. 
all,  or  some  of  the  hydrogen  in  the  latter,  but  none  of  that  in 
the  former,  is  replaceable  by  metal  when  the  compound  is 
acted  on  by  a  metallic  carbonate, — hence  we  infer  that  the 
function  discharged  by  a  given  atom  in  a  molecule  depends 
not  only  on  the  nature  of  that  atom,  but  also  on  the  nature  of 
the  atoms  with  which  it  is  directly,  and  indirectly,  connected 
in  the  molecule. 

In  all  the  alcoholic  groups  (viz.  H2C-OH,  HC-OH, 
and  C  —  OH)  an  atom  of  hydrogen  is  directly  connected 
with  an  oxygen  atom  which  is  again  connected  with  an 
atom  of  carbon,  within  the  binding-sphere  of  which  come 
either  hydrogen  atoms  and  atoms  belonging  to  the  other 
part  of  the  molecule — always  either  carbon  or  hydrogen 
atoms — or  only  the  latter.  In  the  acid  group  (O  —  C  —  OH) 
the  carbon  atom  with  which  the  hydrogen  atom  is  indirectly 
connected  (through  an  atom  of  oxygen)  is  itself  directly 
connected  with  an  oxygen  atom,  as  well  as  with  an  atom, 
or  atoms,  belonging  to  the  other  part  of  the  molecule. 
Now  oxygen  is  a  markedly  electro-negative  element ;  from 
the  facts  enumerated  and  from  other  similar  facts,  the  gene- 
ralisation has  been  made,  that  when  an  atom  of  hydrogen  is 
within  the  binding-sphere  of  an  atom  of  carbon,  which  also 
directly  binds  negative  atoms,  or  negative  groups  of  atoms, 
that  hydrogen  is,  as  a  rule,  ' replaceable  by  metal/  &c.,  i.e. 
that  hydrogen  fulfils  the  function  of  'acid  hydrogen1.' 

1  I  am  aware  that  such  expressions  as  are  used  in  these  paragraphs,  *  a  carbon 
atom  is  directly  connected  with,'  or  'directly  binds  to  itself,  an  atom  of  hydrogen;' 
'an  atom  of  hydrogen  comes  within  the  binding-sphere  of  a  carbon  atom,'  &c.,  are 
very  easily  misunderstood ;  they  appear,  at  first  sight,  to  convey  much  more  pre- 
cise information  than  they  really  do  convey.  I  have  more  than  once  insisted  on 
the  importance  of  clearly  remembering  that  these  and  similar  expressions  are 
attempts  to  summarise  facts  concerning  the  actions  of  compounds  in  terms  of  a 
special  theory  of  the  structure  of  compounds.  Nor  should  it  be  forgotten  that, 
granting  the  fundamental  hypotheses  of  the  molecular  theory,  and  also  granting 


I5O  CHEMICAL   STATICS.  [§  75 

75.  In  thus  trying  to  use  the  theory  of  valency  as  a  guide 
towards  determining  the  structures  of  isomeric  molecules,  we 
have  found  it  on  the  whole  advantageous  to  limit  this  theory 
in  various  ways. 

I.  The  theory  is  applied  in  strictness  only  to  mole- 
cules of  gases. 

II.  The  valency  of  an  atom  is  defined  as  a  number 
which  expresses  the  maximum  number  of  other  atoms  be- 
tween which  and  the  given  atom  there  is  direct  action  and 
reaction  in  a  molecule ;   this  number  is  determined  by  the 
study  of  certain  defined  classes  of  molecules. 

III.  Isomerism  is  regarded  as  correlated  with  varying 
relative  positions  of  atoms,  not  with  variations  in  the  distances 
between  identically  arranged  atoms,  in  any  molecule. 

Applying  the  theory  as  thus  limited,  and  for  the  most  part 
to  compounds  of  carbon,  we  found  that  the  structural  formulae 
of  classes  of  carbon  compounds  can  be  so  far  generalised  as  to 
admit  of  the  assertion  that  the  molecules  of  the  members  of 
any  one  class  are  characterised  by  the  presence  of  a  special 
atomic  group  which  may  be  called  the  class-group  ;  and  that 
hence  the  first  step  in  assigning  a  structural  formula  to  a  new 
compound  is  to  determine,  by  a  comparison  of  the  reactions  of 
this  compound  with  those  of  known  substances  belonging  to 
various  classes,  the  class  to  which  it  belongs  :  having  done 
this,  we  then  eliminate  from  the  possible  structural  formulae 
those  which  do  hot  contain  the  characteristic  group  of  the 
class  in  which  our  compound  is  placed.  Finally,  we  choose 
from  the  remaining  formulae  that  one  which  best  summarises 
the  reactions  of  the  compound  molecule  under  consideration 
and  its  relations  to  other  molecules. 

We  found  that  a  wide  knowledge  of  the  characters  of  classes 
of  compounds  is  required  on  the  part  of  him  who  would 
employ  this  method  with  success,  and  also  that  the  chemist 

that  each  atom  can  act  directly  on  only  a  limited  number  of  other  atoms  in  a 
molecule,  we  are  obliged  to  regard  the  atoms  which  form  any  molecule  as  per- 
forming constant  but  regulated  movements,  and  not — as  might  be  supposed  by  a 
careless,  or  superficial  reader  of  the  atomic  explanation  of  isomerism — as  in  abso- 
lutely fixed  positions  within  the  molecule. 


§§  7&>  77]        ATOMIC   AND   MOLECULAR  SYSTEMS.  1 5 1 

has  constantly  to  be  on  his  guard  against  drawing  too  rigid 
conclusions.  A  new  compound  may  represent  a  new  class, 
hence  a  new  class-group  has  to  be  determined  by  comparing  the 
reactions  of  the  new  compound  with  those  of  others  the  classifi- 
cation of  which  is  fairly  settled,  and  also  by  seeking  to  obtain 
other  representatives  of  the  new  class.  The  discovery  and 
study  of  new  compounds  apparently  belonging  to  a  known 
class  may  lead  to  a  revision  of  the  general  formula  assigned 
to  the  class,  and  perhaps  to  a  division  of  the  class  into  sub- 
classes, each  characterised  by  its  own  group. 

76.  The  application  of  the  theory  of  valency  to  deter- 
mine the  most  probable   of  many  possible  formulae  is  evi- 
dently a  matter  of  no  little  difficulty.     Certain  generalisations 
are  usually  adopted  as  guides  in  interpreting  the  results  of  the 
study  of  the  'chemical  habitude'  of  molecules.     The  principal 
generalisations  are  these. 

(1)  '  Those  atoms  which  are  obtained  as  an  undecom- 
'  posed  group  in  the  analysis  of  a  compound,  are  contained  in 
'  the  molecule  of  that  compound  as  a  group  of  directly  com- 
'  bined  atoms.' 

(2)  'When  a  group  of  atoms  passes  from  one  com- 
'  pound  molecule  to  another,  the  relative  arrangement  of  these 
'  atoms  is  not,  as  a  rule,  altered.' 

(3)  '  When  an  atom,  or  group  of  atoms,  replaces  another 
'  atom  or  group  of  atoms  of  equal  valency  with  itself,  the  re- 
'  placing  atom,  or  group,  occupies  (as  a  rule)  the  same  position 
'  relatively  to  the  other  atoms  in  the  molecule  as  was  occupied 
'by  the  atom,  or  group  of  atoms,  which  it  has  replaced1.' 

77.  Many  of  the  reactions  given  on  pp.  144 — 146,  as  illus- 
trative of  methods  for  assigning  structural  formulae  to  given 
compounds,  also  serve  as  illustrations  of  the  use  of  these  gene- 
ralisations ;  one  or  two  further  illustrations  will  be  given  here. 

Two  isomerides, 

(!)    CH3  (2)    CH3 

CH2        and  O 

OH  CH3 

1  L.  Meyer,  loc.  cit.  pp.  251  et  seq. 


152  CHEMICAL  STATICS.  [§77 

.having  each  the  formula  C2H6O  are  theoretically  possible1. 
Two  compounds  having  this  formula  are  known.  One  of  these 
(alcohol)  is  acted  on  by  potassium  or  sodium  thus, 

(a)     C2H60  +  K  =  C2H5KO  +  H; 

potassium  (or  sodium)  does  not  act  on  the  substance  thus 
formed  :  alcohol  is  acted  on  by  phosphorus  pentachloride 
thus, 

(ff)     C2H60  +  PC15=C2H5C1  +  POC13  +  HC1. 

The  second  isomeride  (methyl  ether)  is  not  acted  on  by 
potassium  or  sodium  but  reacts  with  phosphorus  penta- 
chloride thus, 

C2H6O  +  PC15=2CH3C1+POC13. 

The  first  formula  generalises  the  reactions  of  alcohol,  the 
second  generalises  the  reactions  of  methyl  ether ;  thus 
(a}     CH3  CH3 

CH2+K=CH2+H, 
OH  OK 

one,  and  only  one,  hydrogen  atom  is  represented  in  the 
formula  as  indirectly  bound  (through  an  oxygen  atom)  to 
a  carbon  atom  ; 

(0)    CH3  CH3 

CH2  +  PC16=CH2  +  POC13+HC1, 
OH  Cl 

the  group  OH  is  replaced  by  the  atom  Cl,  which  being  of 
equal  valency  is  regarded  as  occupying  the  place  in  the  mole- 
cule relatively  to  the  other  atoms,  formerly  occupied  by  the 
group  OH. 

The  second  formula  H3C  — O  — CH3  assigned  to  methyl 
ether,  represents  all  the  hydrogen  atoms  as  directly  acting 
on  atoms  of  carbon,  they  have  all  the  same  function  ;  but  the 
oxygen  atom  is  linked  only  to  carbon,  if  it  is  replaced  by 
two  monovalent  atoms,  e.g.  by  chlorine,  the  molecule  can  no 

1  See  Lothar  Meyer,  loc.  cit.  pp.  252  et  seq. 


§77]  ATOMIC  AND   MOLECULAR   SYSTEMS.  153 

longer  hold  together  but  separates  into  two  molecules,  each 
having  the  structure  Cl  —  CH3. 

When  the  molecule  HO  —  CH2—  CH3  is  oxidised,  it  loses 
two  atoms  of  hydrogen,  producing  C2H4O,  which  is  then 
changed,  by  taking  up  one  atom  of  oxygen,  into  the  new 
molecule  C2H4O2.  Probably  the  simplest  way  in  which  these 
changes  can  be  represented  in  structural  formulae  is 

(i)    CH3  CH3  (2)    CH3  CH3 

CH2  — H,  =  C  C      +O  =  C  — O. 

II  I  I 

OH  OH  OH  OH 

But  when  the  molecule  C2H4O2  is  acted  on  by  phosphorus 
pentachloride  it  yields  C2H3OC1,  and  this  is  unacted  on  by  the 
same  reagent :  C2H4O2  is  a  monobasic  acid,  when  its  sodium 
salt  is  heated  with  caustic  soda  it  is  decomposed  thus, 

C2H3Na02+ NaHO  =  Na2CO3  +  CH4. 
These  reactions  are  all  expressed  by  the  formula1  O  — C  — CH3 

OH 

which  is  therefore  adopted  as  the  structural  formula  for  acetic 
acid.  But  when  the  compound  C2H4O  (intermediate  between 
alcohol  and  acetic  acid)  is  acted  on  by  phosphorus  penta- 
chloride it  yields  C2H4C12,  and  not  C2H3C1  as  might  be  ex- 
pected if  the  formula  OH  — C  — CH3,  provisionally  assigned 
to  it,  were  correct.  From  synthetical  and  analytical  reactions, 
CaH4Cl2  may  be  shewn  to  be  best  represented  by  the  structural 
formula  C12  =  CH  —  CH3 ;  assuming  this  formula,  and  re- 
membering that  the  reaction  to  be  explained,  viz.  formation 
of  this  compound  from  C2H4O,  consists  in  the  replacement  of 

1  Thus, 
(i)    CH3  CH3  (2)    CH3  CH3 

C— O  +  PCL  =  C— O  +  &c.          C— O  +  Na— OH   =  H  +  Na2CO3. 

I  !  I 

OH  Cl  ONa 

One  of  the  carbon  atoms  in  the  original  molecule  remains  associated  with  3  atoms 
of  hydrogen  throughout  both  processes  of  change,  hence  we  conclude  that  the 
molecule  of  acetic  acid  contains  the  group  CH3. 


1 54  CHEMICAL   STATICS.  [§  77 

one  divalent  oxygen  atom  by  two  monovalent  chlorine  atoms, 
we  apply  generalisation  (3),  par.  76,  and  conclude  that  the 
structure  of  the  molecule  C2H4O  is  best  represented  by  the 
formula  O-.CH-CHa. 

The  oxidation  of  alcohol  must  then  it  appears  be  repre- 
sented thus  in  structural  formulae, 

(i)    CH3  CH3  (2)    CH3  CH3 

CH2  — H2  =  C  — H  C  — H  +  0   =  C  — OH. 

O— H  O  O  O 

Another  and  somewhat  more  complex  illustration,  taken 
from  the  so-called  '  aromatic '  carbon  compounds,  will  serve  to 
shew  that  the  generalisations  stated  in  par.  76,  although 
widely  applicable,  must  yet  be  used  with  great  caution.  As- 
suming the  generally  adopted  structural  formula  for  benzene1 
(C6H6),  viz.2 

H 
I 

H.  —  C/    ^C  —  H 

I  I 

H  — Cx    /C  —  U 

I 

H 

the  existence  of  three,  and  only  three  isomeric  dichloro-  or 
dibromo-,  &c.,  benzenes  becomes  possible,  viz. 

(I)  (2)  (3) 

C  — Cl  C-C1                                C  — Cl 

/  \  /  \                                    /  \ 

H  — C      C  — Cl  H  — C      C  — H  H  — C      C  — H 

II  II                                   II". 

H  — C      C  — H  H  — C      C  — Cl  H  — C      C  — H 

XX  \  /                                      \  / 

C  C                                          C 

I  I  I 

H  H  Cl 

1  See  Armstrong  and  Groves,  /of.  cit.  pp.  260 — 63  ;  also  pp.  270 — 74.  See  also 
post,  pp.  163 — 165,  par.  81. 

3  The  fact  that  this  formula  is  generally  used  rather  than  the  more  complex 
formula  originally  proposed  by  Kekule  with  alternate  'doubly'  and  'singly-linked' 


§77]  ATOMIC   AND   MOLECULAR   SYSTEMS.  155 

In  (i)  both  chlorine  atoms  are  within  the  binding-spheres  of 
carbon  atoms  which  are  directly  bound  to  one  another  ;  in  (2) 
one  carbon  atom,  and  in  (3)  two  carbon  atoms  intervene 
between  those  atoms  of  carbon  within  whose  binding-spheres 
the  chlorine  atoms  are  found. 

These  three  isomeric  compounds  are  usually  distinguished 
as  1:2,  i  :  3,  and  I  :  4  dichlorobenzene  ;  it  is  evident  that 
I  :  61  =  i  :  2,  and  1:5  =  1:3.  Each  of  these  dichloroben- 
zenes  when  acted  on  by  chlorine  yields  one  or  more  isomeric 
trichlorobenzenes  (C6H3C13).  Korner  has  formulated  a  simple 
method  of  proving  that  I  :  2  dichlorobenzene  can  yield  two, 
i  :  3  can  yield  three,  and  I  :  4  can  yield  only  one  trichloro- 
benzene2. 

Now  if  the  generalisations  we  are  considering  are  applic- 
able to  the  'aromatic1  hydrocarbons,  it  follows  that  any 
diderivative  of  benzene  —  C6H4^T2  where  X  is  a  monovalent 
atom  or  group  of  atoms  —  which,  by  a  simple  series  of  reac- 
tions can  be  obtained  from,  or  can  be  converted  into  I  :  2 
dichloro-  (or  dibromo-,  or  dinitro-)  benzene,  must  be  itself  a 
i  :  2  derivative,  i.  e.  the  two  X  groups  or  atoms  must  be  within 
the  binding-spheres  of  carbon  atoms,  between  which  there  is 
direct  mutual  action  within  the  molecule.  A  similar  conclu- 
sion is  drawn  regarding  the  structure  of  those  compounds  of 
the  formula  C6H4^Y"2  which  can  be  obtained  from  or  reduced 
to  i  :  3,  or  1:4  dichloro-,  &c.,  benzene. 

carbon  atoms,  and  that  most  chemists  are  content  meanwhile  to  overlook  the 
contradiction  involved  in  employing  such  a  formula  and  yet  holding  the  theory  of 
'bonds,'  is  indicative  of  the  unsatisfactory  nature  of  this  theory  when  rigidly 
applied. 

1  The  carbon  atoms  in  the  hexagon  are  numbered  thus  : 


6  C       C  2 

\         \ 
5  C       C  3 


4 

2  i  :  2  yields  1:2:3,  and  1:2:4(1:2:3  =  1:2:6,  and  1:2:5  =  1:2:4). 
i  :  3  yields  1:2:3,  and  1:3:4  (which  =  i  :  3  :  6),  and  1:3:5.  1:4  yields  1:2:4 
(which  =1:3:4,  =1:4:5  =  1:4:6).  See  Armstrong  and  Groves,  loc.  cit.  pp. 
267—8. 


156  CHEMICAL   STATICS.  [§  77 

Thus  I  :  3  dinitrobenzene,  by  the  action  of  zinc  and 
hydrochloric  acid,  yields  nitramidobenzene  C6H4NO2NH2; 
by  the  further  action  of  nascent  hydrogen  this  yields 
diamidobenzene  C6H4(NH2)2,  which,  by  the  'diazo  reac- 
'tion1'  (or  '  Griess'  reaction'),  yields  bromohydroxybenzene 
C6H4Br .  OH,  this  compound  is  therefore  assumed  to  be  a  1:3 
derivative  of  benzene.  Now  when  this  body  is  fused  with 
caustic  potash  it  yields  one  of  the  three  isomeric  dihydroxy- 
benzenes  C6H4(OH)2;  in  accordance  with  generalisation  (3), 
par.  76,  this  dihydroxybenzene  will  be  regarded  as  a  1:3 
derivative.  But  I  :  4  bromohydroxybenzene — obtained,  by  a 
method  similar  to  that  sketched  above,  from  I  :  4  dinitroben- 
zene— yields,  by  fusion  with  potash,  the  same  dihydroxy- 
benzene as  just  mentioned  ;  hence  this  body  is  now  shewn  to 
be  probably  a  I  14  derivative.  Again,  I  :  4  C6H4I .  OH  when 
fused  with  potash  at  a  high  temperature  yields  only  the 
dihydroxybenzene  in  question,  but  at  165°  it  yields  only  one 
of  the  isomeric  molecules2. 

Another  example,  shewing  how  necessary  it  is  to  apply 
such  generalisations  as  those  under  consideration  only  in  a 
tentative  manner,  is  furnished  by  some  reactions  of  I  :  4  nitro- 
bromobenzene  (C6H4NO2Br).  By  the  action  of  alcoholic  am- 
monia on  this  compound  nitramidobenzene  (C6H4NO2NH2) 
is  produced ;  that  this  nitramidobenzene  is,  as  we  should 
expect,  a  1:4  derivative  can  be  proved  by  trustworthy  evi- 
dence :  but  if  the  same  I  :  4  C6H4NO2Br  is  acted  on  by  potas- 
sium cyanide,  and  the  product  of  this  action  (C6H4CNBr)  is 
boiled  with  dilute  acid,  a  bromobenzoic  acid  [C6H4Br(CO2H)] 
is  obtained,  which  on  account  of  its  reactions  must  be  re- 
garded as  a  1:3,  and  not  a  1:4,  derivative  of  benzene. 
Similarly  the  action  of  potassium  cyanide  followed  by  that  of 
dilute  acid  on  I  :  3  C6H4NO2Br  does  not  yield  (as  a  strict 
application  of  the  statement  in  par.  76  would  lead  us  to  ex- 
pect) i  :  3,  but  1:2  C6H4Br .  CO2H.  And,  finally,  when  I  :  2 

1  For  an  account   of  these  '  diazo-reactions,'  which   are   much   used   in   the 
synthesis    of   benzene    derivatives,    see    Armstrong    and    Groves,    loc.   cit.    pp. 
298—9. 

2  See,  for  more  details,  Armstrong  and  Groves,  loc.  cit.  pp.  521 — 2. 


§§  78»  79]        ATOMIC   AND    MOLECULAR   SYSTEMS.  157 

CGH4NO2Br  is  subjected  to  the  action  of  potassium  cyanide1 
no  replacement  of  NO2  by  CN  occurs2. 

78.  The    application   of  the   theory   of  valency   to  the 
phenomena  summed  up  in  the  term  isomerism  has  rendered 
more  definite  that  general  conception  of  the  molecule  as  a 
structure  which  arose  so  soon  as  it  was  recognised  that  each 
atom  in  a  molecule  could  act  directly  on  a  limited  number  of 
other   atoms.      Analyses    of  reactions,    and   comparisons   of 
classes  of  reactions,  have  led  to  the  adoption  of  certain  rules 
which,  when  applied  with  caution,  have  proved  of  very  con- 
siderable service  in  researches  on  molecular  structure.     These 
researches  have  served  to  emphasise  the  fundamental  con- 
nection  which   exists   between    composition    and  properties, 
between    function    and    quality   of  material :    but   chemistry 
is  not  now  contented  with  connecting  the  reactions  of  com- 
pounds with  their  elementary  composition,  or  even  with  the 
atomic   composition   of  their   molecules,   she   attempts,   and 
is  gradually  succeeding  in  the  attempt,  to  connect  certain 
definite   arrangements  of  atoms   in   molecules   with   certain 
definite  properties  and  actions  of  these  molecules. 

79.  In  his  remarkable  paper  published  in   1858,  Kekule 
recognised  that  the  function  performed  by  an  atom  in  any 
molecule  depends  on  the  nature  of  the  other  atoms,  as  well  as 
on  the  nature  of  the  given  atom,  and  also  on  the  arrangement 
of  all  the  atoms.     Since  1858  the  nature  of  the  dependence  in 
question  has  been   more  fully  elucidated ;    and  although  it 
cannot  be  said  that   we   have  at  present  much  knowledge, 
capable  of  being  generalised  in  statements  at  once  accurate 
and  wide,  of  the  connections  between  the  functions  of  parts 
of  molecules  and  the  atomic  composition  and  structure  of 

1  In  Armstrong  and  Groves,  loc.  cit.  pp.  334 — 6  will  be  found  an  account  of  the 
action  of  potassium  cyanide   on  benzene  derivatives;   this  action,  although  ab- 
normal, may  be  expressed  by  a  tolerably  simple  generalisation. 

2  Further  examples  of  the  point  under  discussion  will  be  found  in  the  change 
of  normal  propyl  to  isopropyl,  by  (i)  action  of  Al2Br6  [see  Kekule,  Ber.  12.  2279] 
or  (2)  action  of  zinc  dust  [see  Jacobsen,  Ber.  12.  1512]:   also  in  the  change  of 
CnH2n+1CN  to  CnH2n+!NC  by  the  action  of  heat :  and  also  in  the  action  of 
reducing  agents  on  phenanthraquinone  [see  Japp,  C.  S.  Journal  Trans,  for  1883. 
13,  note]. 


158 


CHEMICAL   STATICS. 


79,  80 


these  molecules,  yet  we  are  certainly  gathering  facts  which 
will  doubtless  prove  the  basis  for  far-reaching  generalisations. 

Numerous  illustrations  have  already  been  given  of  the 
existence  of  a  connection  of  some  kind  between  the  functions 
of  parts  of  a  molecule  and  the  composition,  using  this  term  in 
its  widest  sense,  of  the  whole  molecule.  But  the  fact  of  the 
existence  of  such  a  connection  is  so  important  that  I  wish  to 
devote  a  paragraph  to  its  illustration. 

The  relation  to  be  illustrated  is  that  between  the  function 
performed  by  an  atom,  or  atomic  group,  in  a  molecule, 


and 


I.  The  nature,  and  arrangement,  relatively 

to  the  given  atom  (or  group),  of  the 
other  atoms, 

II.  The  general  relative  arrangement  of  all 

the  parts, 


in  the 
mole- 
cule. 


80.  I.  That  the  function  performed  by  an  atom  of 
hydrogen  in  a  molecule  varies  according  to  the  nature  and 
arrangement  relatively  to  the  hydrogen  of  the  other  atoms, 
has  already  been  shewn  (see  par.  74,  pp.  147 — 149).  Hydrogen 
which  is  associated  with  negative  atoms  or  groups  is  as  a  rule 
'  replaceable  by  metals/  in  other  words,  performs  acid  functions 
in  the  molecule.  Thus  of  the  two  compounds,  potassium- 
nitropropane  and  bromo-nitropropane,  the  latter  is  much 
more  decidedly  acid  than  the  former :  if  the  formulae  are 
compared, 


K 

I 

H6C2-C-N02 

H 


Br1 

I 
with  H5C2  — C  — NO2, 


H 


1  The  reaction  of  formation  of  bromo-nitropropane  affords  a  very  interesting 
example  of  the  modifying  influence  of  one  atom  on  another  in  a  molecule :  bro- 
mine does  not  replace  hydrogen  in  nitropropane,  but  when  an  atom  of  hydrogen 
in  the  nitropropane  molecule  is  replaced  by  potassium,  the  product  is  readily  acted 
on  by  bromine  with  substitution  of  an  atom  of  the  very  positive  potassium  by  an 
atom  of  the  very  negative  bromine 

[C2H5.CHK.N02  +  Br2  =  C2H5.CHBr.N02 
(See  Armstrong  and  Groves,  loc.  tit.  pp.  166 — 7.) 


§  80]  ATOMIC  AND   MOLECULAR  SYSTEMS.  159 

it  is  seen  that,  in  the  markedly  acid  compound,  the  carbon 
atom  with  which  the  sixth  atom  of  hydrogen  is  represented 
as  directly  connected  is  itself  directly  bound  to  the  negative 
group  NO2  and  to  the  negative  atom  Br ;  but  that,  in  the  less 
acid  compound,  this  carbon  atom  is  represented  as  directly 
bound  to  the  negative  group  NO2  and  to  the  positive  atom  K. 

Again  C  —  H  is  not  an  acid,  but  C  —  H  is ;  the  influence 
I!!  li! 

C13  (N02)3 

of  the  very  negative  NO2  group  seems  to  be  impressed  through 
the  carbon  atom  on  the  hydrogen  atom  of  the  molecule. 

In  these  cases  the  atom  of  '  acid  hydrogen '  is  represented 
as  directly  bound  to  a  carbon  atom  within  the  binding- 
sphere  of  which  come  negative  atoms  or  groups.  But  the 
case  of  the  nitrolic  acids,  assuming  the  usually  accepted 
formula,  viz.  (CMH2B+1) — C  — NO2\  to  be  correct,  shews  that 

N-OH 

an  atom  of  hydrogen  which  is  indirectly  bound  to  carbon 
itself  binding  negative  groups  may  react  as  acid  hydrogen. 
Glyoxaline  and  tribromoglyoxaline  also  furnish  examples 
in  point ;  each  of  these  molecules  contains  one  atom  of  acid 
hydrogen2. 

A  portion  of  the  hydrogen  in  monohydric  alcohols  is  re- 
placeable by  metal,  but  only  by  the  very  positive  metals,  e.g. 

1  It  is  interesting  to  note  that  iso-nitroso  malonic  acid 
C02H 

C— NOH 
I 
C02H 

acts  as  a  dibasic,  not  tribasic,  acid. 
3  The  most  probable  formulae  are, 

N  N 

C— C— C— N— H    and    C— C— C— N— H 

III  III 

H    H    H  Br  Br  Br 

(see  Armstrong  and  Groves,  loc.  cit.  p.  769).  Some  reactions  of  water  are 
consistent  with  the  statement  that  one  of  the  hydrogen  atoms  performs  the 
functions  of  acid  hydrogen ;  e.  g. 

HOH  +  CH3ONa=CH3OH  +  NaOH. 


160  CHEMICAL   STATICS.  [§  So 


C2H5.OH  +  K  =  C2H5OK-f  H;  but  by  the  introduction  of 
an  atom  of  sulphur  in  place  of  oxygen  a  thio-alcohol  is  ob- 
tained which  readily  exchanges  hydrogen  even  for  com- 
paratively negative  metals,  e.g. 

2C2H5  .  SH  +  HgO  =  (C2H5.  S)2Hg  +  H2O\ 

Again,  the  experiments  of  R.  Meyer2  appear  to  prove  that 
an  atom  of  hydrogen  in  the  molecule  of  a  carbon  compound 
can  be  replaced  by  the  group  OH,  by  the  action  of  oxidising 
agents,  only  when  the  carbon  atom  with  which  the  hydrogen 
is  directly  connected  does  not  directly  bind  any  other  hy- 
drogen atoms  ;  thus  isobutyric  acid  is  oxidised  by  potassium 
permanganate  to  isohydroxybutyric  acid,  but  normal  butyric 
acid  yields  acetic,  oxalic,  carbonic  and  other  acids  under  the 
same  conditions. 

O 

[In   structural  formulae,   H3C  —  CH2—  CH2  —  C^         does 

OH 

O  /CH3 

not    yield    an    hydroxy-acid  ;    but  /C  —  CH          yields 

HO 
O  CH 


HO 

Victor  Meyer's  experiments  likewise  appear  to  establish  a 
connection  between  the  structure  of  the  nitro-derivatives  of 
compounds  of  the  general  form  X  —  CH  —  X  (produced  by 
the  action  of  NO.  OH  on  those  compounds)  and  the  relatively 
easy  or  difficult  removal,  in  whole  or  in  part,  of  one  of  the 
X  groups3. 

Further  illustrations  of  the  connections  between  the  func- 
tions of  parts  of  molecules  and  the  nature  and  arrangement  of 
the  other  parts  are  furnished  by  the  reactions  of  (a)  the  nitro- 
derivatives  of  benzene  and  its  homologues4,  (b)  chloro-  and 

1  For  details  concerning  these  reactions  see  Armstrong  and  Groves,  loc.  cit. 
pp.  660  —  i. 

2  Ber.  11.  1787:  12.  2238;  Annaten,  219.  234:  220.  i;  see  also  J.  BREDT,  Ber. 
13.  748. 

3  Ber.  16.  610. 

4  Armstrong  and  Groves,  loc.  cit.  pp.  322  —  5. 


§  80]  ATOMIC  AND   MOLECULAR   SYSTEMS.  l6t 

chloro-nitrobenzenes1,  and  (c)  benzoquinone  and  chloro-ben- 
zoquinone2. 

(a)  Two  hydrogen  atoms  in  the  benzene  molecule  C6H6 
can  be  replaced  by  the  group  NO2  twice,  only  by  the  action 
of  very   concentrated    nitric   acid    mixed   with   concentrated 
sulphuric  acid ;  if  however  an  atom  of  hydrogen  in  C6H6  is 
replaced    by    the    group     CH3,    the    resulting    molecule — 
C6H5.CH3 — is  much  more  readily  converted  into  the  dinitro- 
derivative    C6H3(NO2)2 .  CH3 ;    if   three    hydrogen    atoms    in 
C6H6  are  replaced  by  CH3  three   times,  the  molecule  thus 
formed,  [C6H3(CH3)3]   very  easily  yields  a  /rznitro-derivative 
Q(NO2)3(CH3)3  by  the  action  of  nitric  acid. 

(b)  The  chloro-benzenes,  C6H6_XC1X,  do  not  readily  ex- 
change  chlorine   for  other  atoms ;   but  the  chloro-nitroben- 
zenes,   as   a   class,    by   mere    contact   with    ammonia    yield 
amido-nitrobenzenes,  e.g.  C6H4C1NO2  exchanges  Cl  for  NH2, 
yielding  C6H4(NH2)NO2.     Although  the  action  of  ammonia 
on  the  chloro-nitrobenzenes  generally  results  in  the  exchange 
of  chlorine  atoms  for  the  group  of  atoms  NH2,  nevertheless 
one  of  the  isomeric  molecules  represented  by  the  formula 
C6H2C12(NO2)2   yields    C6H2C12NO2(NH2)   by   the    action    of 
ammonia  upon  it ;  and  similarly  one  of  the  isomeric  bromo- 
trinitrobenzenes,  C6H2Br(NO2)3,  exchanges,  not  its  Br  atom, 
but  one  of  the  NO2  groups,  for  NH2,  under  the  action  of  the 
same  reagent.     Again,  although  the  homologues  of  benzene 
readily  yield  either  chloro-  or  nitro-derivatives,  and  the  chloro- 
derivatives   may  be  readily  nitrated,  yet  hydrogen  in  nitro- 
derivatives  is  not  easily  replaced  by  chlorine. 

(c)  When    benzene     (C6H6)    is    oxidised,   benzoquinone 
(C6H4O2)  is  probably  produced  but  decomposed  again ;  the 
chemical  change  proceeds  further  than  formation  of  benzoqui- 
none.     If  however   benzene  is  acted    on  by  oxidising    and 
chlorinating    reagents   simultaneously,    dichlorobenzoquinone 
(C6H2C12O2)  is  formed  and  can  be  isolated.     The  substitution 
of  chlorine  for  hydrogen  in  the  C6H6  molecule  modifies  the 
function  of  part  of  the  remaining  hydrogen  so  that  it  can  be 

1  Armstrong  and  Groves,  loc.  cit.  pp.  333 — 4. 

2  Ibid.  loc.  cit.  p.  794. 

M.  C.  II 


162  CHEMICAL  STATICS.  [§  8l 

replaced  by  oxygen,  and  at  the  same  time  the  presence  of  C12 
in  place  of  H2  in  the  new  molecule  appears  to  confer  on  it  a 
greatly  increased  stability  towards  oxidising  substances. 

8 1.  II.  A  good  illustration  of  the  influence  exerted  by 
the  arrangement  of  all  the  atoms  in  a  molecule  on  the 
functions  of  one,  or  some,  of  these  atoms,  is  afforded  by  a  com- 
parative study  of  the  two  groups  of  carbon  compounds — more 
especially  the  hydrocarbons — generally  known  as  'fatty'  (or 
1  paraffinoid ')  and  'aromatic'  (or  'benzenoid')  respectively1: 
a  few,  but  only  a  few,  of  the  more  important  points  will  be 
briefly  stated. 

Comparing  the  action  of  concentrated  nitric  or  sulphuric 
acid  on  a  paraffin,  e.g.  C2H6,  with  the  action  of  the  same  acid 
on  a  benzene,  e.g.  C6H6,  it  is  noticed  that  while  one  or  more 
hydrogen  atoms  in  the  molecule  of  the  latter  are  readily 
replaced  by  the  group  NO2  or  SO3H,  the  acid  is  without 
action  on  the  former  hydrocarbon.  When  the  homologues  of 
benzene  are  oxidised  they,  as  a  class,  yield  quinones,  the 
molecule  of  any  one  of  which  contains  the  same  number  of 
carbon  atoms  as  the  parent  hydrocarbon,  but  has  two  atoms 
of  oxygen  in  place  of  two  atoms  of  hydrogen  in  the  original 
molecule.  When  the  paraffinoid  hydrocarbons,  on  the  other 
hand,  are  oxidised,  they  do  not  yield  derivatives  analogous 
to  the  quinones,  but  rather  afford  mixtures  of  acids  the 
molecule  of  each  of  which  contains  a  smaller  number  of 
carbon  atoms  than  were  present  in  the  original  hydrocarbon 
molecule. 

When  chlorine  acts  on  the  molecule  of  a  paraffinoid 
hydrocarbon  containing  only  tetravalent2  carbon  atoms,  it 
produces  chloro-substitution  derivatives  containing  tetravalent 
carbon  atoms,  the  whole  of  the  hydrogen  in  the  hydrocarbon 
being  eventually  replaced  by  chlorine,  the  further  action  of 
chlorine  then  frequently  results  in  a  separation  of  the  mole- 
cule into  two  or  more  molecules,  each  containing  a  smaller 
number  of  carbon  atoms  than  the  original  molecule.  When 
however  chlorine  acts  on  the  molecule  of  a  paraffinoid 

1  See  Armstrong  and  Groves,  pp.  391 — 402. 

2  In  ordinary  nomenclature  it  would  be  said  *  singly-linked  carbon  atoms.' 


§  8l]  ATOMIC  AND   MOLECULAR  SYSTEMS.  163 

hydrocarbon  containing  two  or  more  trivalent1  carbon  atoms 
it  generally  combines  with  it  and  so  produces  a  molecule 
containing  tetravalent  carbon  atoms,  which  is  then  acted  on 
by  chlorine  as  hydrocarbons  with  tetravalent  carbon  atoms 
usually  are. 

Thus,  H3C-CH2-CH3,  by  the  action  of  IC1  gives 
H3C  -  CH2-  CH2C1  &c.,  and  finally  C13C  -  CC12-CC13,  and 
this  octochloropropane  by  the  continued  action  of  IC1  gives 
C13C-CC13  and  CC14 ;  but  H2C-CH2-CH2,  containing 
two  trivalent  carbon  atoms,  by  the  action  of  IC1  gives 
C1H2C  —  CH2  — CH2C1,  containing  only  tetravalent  carbon 
atoms,  by  the  further  action  of  IC1,  C3C18  is  obtained,  and 
this  is  eventually  decomposed  to  C2C16  and  CC14. 

The  action  of  chlorine  on  the  aromatic  hydrocarbon  ben- 
zene (C6H6)  finally  results  in  the  formation  of  hexchloro- 
benzene  C6C16,  in  which,  it  may  be  safely  asserted  from  the 
formula  and  from  a  study  of  the  properties  of  the  com- 
pound, the  carbon  atoms  act  on,  and  are  acted  on  by,  the 
same  number  of  atoms  as  in  the  original  C6H6  molecule.  So 
far  then  benzene  behaves  like  a  paraffin ;  but  IC1  has  no 
action  on  C6C16,  the  molecule  refuses  to  separate  into  parts, 
the  six  atoms  of  carbon  are  apparently  more  firmly  joined 
together,  and  form  a  more  stable  group,  than  the  carbon 
atoms  in  the  molecule  of  a  paraffin. 

The  functions  both  of  the  hydrogen  and  carbon  atoms  in 
the  molecules  of  a  benzene  and  of  a  paraffin — say  in  C6H6 
and  in  C6H14 — evidently  depend  to  some  extent  on  the 
general  arrangement  of  all  the  atoms  in  these  molecules. 

The  arrangement  of  carbon  atoms  supposed  to  characterise 
the  molecule  of  a  fatty  hydrocarbon,  e.g.  a  paraffin,  is  usually 
spoken  of  as  arrangement  in  ' an  open  chain',  while  that  sup- 
posed to  characterise  the  molecule  of  an  aromatic  hydro- 
carbon, e.g.  a  benzene,  is  called  'a  closed  ring2!  If  the  action 

1  In  ordinary  nomenclature  it  would  be  said  '  doubly-linked  carbon  atoms.' 

2  Ring-formed  molecules  resemble  unsaturated   molecules  in  that  they  can 
directly  combine  with  monovalent  atoms  without  loss  of  any  of  their  constituent 
atoms  (e.g.  benzene  forms  C6H6C16);  but  they  resemble  saturated  molecules  in 
that  the  assumption  of  monovalent  atoms  is  possible  only  when  preceded  by  a 

II— 2 


164  CHEMICAL  STATICS.  [§  8 1 

between  atom  and  atom  be  supposed  to  begin  at  one  of  the 
carbon  atoms,  then  in  a  closed  ring  molecule  it  returns  to  that 
atom ;  in  other  words  each  carbon  atom  acts  on,  and  is  acted 
on  by,  at  least  two  other  carbon  atoms  in  the  molecule :  but 
in  an  open  chain  molecule  the  action  does  not  return  to  the 
carbon  atom  at  which  it  started ;  in  other  words,  there  are 
two  carbon  atoms  in  the  molecule,  each  of  which  acts  on,  and 
is  acted  on  by,  only  one  other  carbon  atom. 

The  ring-formed  molecule  containing  six  carbon  atoms 
may  be  represented  thus, 

C 

/  \ 

C  — C  — C  or  thus  C      C 

II  II 

c-c-c  c    c 

\  / 
C 

and  the  open  chain  molecule  thus : 

C  — C  — C  — C  — C  — C. 

As  the  six  carbon  atoms  in  the  molecule  of  benzene  ap- 
pear to  form  a  very  stable  group,  they  are  sometimes  spoken 
of  as  the  '  six-carbon-nucleus '  of  the  molecule.  Now  if  the 
monochloro-derivative  of  xylene  (C8H10)  produced  by  the 
action  of  chlorine  on  that  hydrocarbon  when  cold  is  compared 
with  the  monochloro-derivative  produced  by  the  action  of 
chlorine  on  the  same  hydrocarbon  when  hot,  it  is  found  that 
the  latter  readily  exchanges  its  chlorine  atom  for  the  group 
OH  with  production  of  an  alcohol  (C8H9(OH)),  but  that  the 
chlorine  atom  in  the  former  can  scarcely  be  replaced  by  other 
radicles.  If  we  assume  the  ordinarily  accepted  structural 
formulae  for  the  two  isomeric  monochloroxylenes  we  at  once 

rearrangement  of  the  mutual  actions  between  some  of  the  polyvalent  atoms  (see 
e.  g.  formula  of  benzene  on  p.  154).  (Lossen.) 

The  number  of  molecules  produced  in  any  reaction  wherein  only  saturated 
molecules  take  part  is  equal  to  or  greater  than  the  number  of  molecules  taking 
part  in  the  reaction :  when  the  number  produced  in  any  reaction  is  smaller  than 
the  number  of  molecules  originally  taking  part  in  the  reaction,  at  least  one  of  the 
reacting  molecules  must  be  either  unsaturated  or  ring-formed.  (Lossen.) 

It  is  evident  that  a  ring-formed  molecule  must  contain  at  least  three  polyvalent 
atoms,  and  that  for  such  molecules  n±  <  nz  +  2W4  4-  &c. . . .  +  2. 


§  8l]  ATOMIC  AND  MOLECULAR   SYSTEMS.  165 

see  how  profoundly  the  functions  of  the  chlorine  atoms  depend 
on  the  relative  arrangement  of  all  the  atoms  in  the  molecule. 
The  formulas  in  question  are  (a)  monochloroxylene  from  hot 

xylene, 

H         H2    H2 
/^\       ||      M 
HC       C  —  C  —  C  —  Cl, 

I         I 
HC       CH 

^^ 
H 

(b]  monochloroxylene  from  cold  xylene, 

HC         H2 

<  \       || 
HC      C  —  C  —  CH3. 

I        I 
HC      C  —  Cl 

\  / 
CH 

The  chlorine  atom  in  (a)  is  said  to  be  in  '  the  side  chain! 
and  in  (b)  in  the  '  central  nucleus'  In  the  hydrocarbon  C8H10 
we  have  the  properties  both  of  a  paraffin  and  a  benzene  ;  part 
of  the  molecule,  the  six-carbon-nucleus,  behaves  as  a  ben- 
zenoid  molecule;  the  other  part,  the  side  chain  (C2H5)  as  a 
paraffinoid  molecule. 

A  comparison  of  some  of  the  reactions  of  metallic  hy- 
droxides, alcohols,  and  phenols,  will  serve  to  illustrate  the 
dependence  of  the  functions  of  part  of  a  molecule,  at  once  on 
the  nature  and  arrangement  (relatively  to  this  part)  of  the 
other  atoms,  and  also  on  the  general  arrangement  of  all  the 
atoms,  in  the  molecule. 

The  action  of  acids  on  metallic  hydroxides  and  alcohols 
results  in  the  formation  of  salts  ; 


f  Zn(OH)2  +  2HCl=ZnCl2 
Q'g'  1CH3(OH)+  HC1  =  CH3.C1  +  H20, 

but  phenols  do  not  yield  analogous  products  by  this  reaction. 
Alcohols  and  some  metallic  hydroxides  —  e.g.  Zn(OH)2  and 
A12(OH)6  —  yield  unstable  metallic  derivatives  by  the  action  of 
markedly  positive  metals  or  their  hydroxides  ;  phenols  however 
yield  much  more  stable  metallic  derivatives  by  the  action  of  the 


1 66  CHEMICAL  STATICS.  [§  8 1 

same  metals,  their  hydroxides  or  carbonates.  The  hydrogen 
atom  (or  atoms)  which  is  indirectly  connected,  through  oxygen, 
with  the  metal  or  hydrocarbon-radicle  of  these  molecules, 
evidently  fulfils  more  or  less  acid  or  basic  functions,  ac- 
cording to  the  nature  of  the  other  part  of  the  molecule. 
When  that  other  part  is  a  metallic  atom  (or  atoms)  the 
hydrogen  is  as  a  rule  'basic/  but  in  certain  cases  it  is  also 
feebly  acid ;  when  the  nonhydroxylic  part  of  the  molecule  is 
composed  of  carbon  and  hydrogen  atoms  arranged  in  an 
'open  chain,'  the  hydrogen  appears  to  be  analogous  to  the 
hydrogen  of  metallic  hydroxides,  and  when  the  carbon  and 
hydrogen  are  arranged  in  a  '  closed  ring '  the  hydrogen  ap- 
pears to  be  more  distinctly  acid  in  function1* 

The  following  facts  and  generalisations  concerning  the 
action  of  reagents  on  various  benzene  derivatives  afford 
further  examples  of  the  influence  exerted  by  relative  position, 
and  nature  of  parts  of  a  molecule,  and  general  arrangement 
of  all  atoms  in  a  molecule,  on  reactions  wherein  atoms  (or 
atomic  groups)  in  the  molecule  are  substituted  by  other 
atoms  or  groups. 

In  the  production  of  certain  disubstituted  derivatives 
of  benzene,  C^l^XX',  from  monosubstituted  derivatives, 
C6H5Jf,  it  is  found  that  whether  the  diderivative  shall  belong 
to  the  I  :  2,  i  :  3,  or  I  :  4  series2,  depends  on  the  nature  of 
the  atom,  or  atomic  group  Jf,  in  C6H5Jf,  and  also  on  the 
nature  of  the  atom,  or  group  X',  in  C&H±XX'.  When  X  =  Cl, 
Br,  I,  OH,  CH3  or  NH2,  and  X'  =C1,  Br,  I,  NO2  or  SO3H, 
the  diderivative  C6H4JTJf '  generally  belongs  to  the  I  :  4  series  ; 
when  Jf=NO2,  SO3H  or  CO2H,  and  JT  =  C1,  Br,  .1,  NO2  or 
SO3H,  then  C&H^XXf  generally  belongs  to  the  I  :  3  series3. 

Derivatives  of  benzene  containing  paraffinoid  radicles  as 
'  side  chains,'  when  oxidised,  yield  mono-,  di-,  tri-,  &c.,  basic 
acids,  according  to  the  number  of  side  chains  in  the 
original  molecule;  thus  C6H4.C2H5.CH3  yields  C6H4(CO2H)2, 
C6H4.CHS.C02H  also  yields  C6H4  (CO2H)2>  &c.,  but  if  a 

1  See  Armstrong  and  Groves,  loc.  cit.  p.  566. 

2  See  par.  77,  p.  155  for  an  explanation  of  this  notation. 

3  See  table  in  Armstrong  and  Groves,  loc.  cit.  p.  337. 


§  8l]  ATOMIC  AND   MOLECULAR  SYSTEMS.  l6/ 

negative  atom  or  group  is  introduced  into  the  benzene 
derivative  and  the  oxidation  is  then  effected,  the  paraffin- 
radicle  which  forms  the  side  chain  nearest  to1  the  negative 
atom  (or  group)  is  protected  by  that  atom  (or  group)  and  does 
not  undergo  oxidation.  Thus  C6H4.CH3.C2H5  [i  14]  when 
oxidised  produces  C6H4(CO2H)2,butC6H3.Br.CH3.C2H5[i:  2:4] 
produces  C6H3Br.CH3.CO2H  [i:2:  4].  So  again  C6H4(C2H5)2 
[1:4]  oxidises  to  C6H4(CO2H)2,  but  C6H3.C2H5.SO2NH2.C2H5 
[1:2:4]  oxidises  to  C6H3.C2H5.SO2NH2?CO2H  [i  12:4],  in  this 
case  the  C2H5  nearest  to  the  negative  group  is  protected, 
while  the  other  C2H5  group  undergoes  oxidation  to  CO2H2.. 
So  also  if  1:3:4,  1:4:5  or  1:2:4  dimethylnitroxylene 
(C8H7.CH3.CH3.NO2)  is  oxidised,  in  each  case  the  CH3  group 
nearest  to  the  NO2  group  is  unchanged,  and  the  other  CH3 
group  is  oxidised  to  CO2H :  but  if  the  1:3:5  dimethylnitro- 
xylene is  oxidised,  both  the  CH3  groups  are  converted  into 
CO2H  groups ;  now  in  a  1:3:5  derivative  the  substituting 
groups  are  equally  distributed,  in  the  case  before  us  each 
methyl  group  is  situated  in  exactly  the  same  position  relatively 
to  the  NO2  group3. 

Once  more,  by  the  action  of  chlorine  or  bromine  on  aniline, 
trichlor-  or  tribromaniline  is  produced :  when  I  :  2  or  1:4 
monochlor-  monobrom-  or  mononitraniline  is  chlorinated, 
2  atoms  of  chlorine  are  taken  up  by  the  molecule  in  place  of 
2  atoms  of  hydrogen ;  when  i :  2  or  I  :  4  dichlor-  &c.  aniline  is 
chlorinated,  one  atom  of  chlorine  is  taken  up,  so  that  in  every 
case  the  total  number  of  negative  atoms  in  the  molecule  is  3, 

1  'Nearest  to;'  compare  the  structural  formulae  for  the  three  methylbromo- 
benzenes 

CH^         CH. 

Br 

Br 
1:2  1:3  1:4 

the  Br  atom  is  said  to  be  nearer  to  the  CH3  group  in  the  i :  i  than  in  the  1:3, 
and  nearer  in  the  i  :  3  than  in  the  i  :  4. 

2  See  Remsen  and  Hall,  Amer.  Ghent.   Journal  2.   50;    and  Remsen  and 
Noyes-, -loc.  dt.4i.  197 .  • 

3  See  E.  Wroblewsky,  Ber.  15.  1021. 


1  68  CHEMICAL    STATICS.  [§  8  1 

which  is  also  the  number  of  negative  atoms  that  can  be  sub- 
stituted for  hydrogen  in  the  molecule  of  aniline  itself.  But 
when  1  :  3  monochlor-,  &c.  aniline  is  chlorinated,  3  atoms  of 
chlorine  are  substituted  for  3  of  hydrogen,  and  when  I  :  3 
dichlor-,  &c.  aniline  is  chlorinated  3  atoms  of  chlorine  are 
still  taken  up.  Thus 

C6H5.NH2  by  chlorination  yields  C6H2C13.NH2 

i  :  2  or  i  :  4  C6H4C1  .  NH2  yields  C6H2C13.  NH2 
i  :  2  or  i  :4  C6H3C12.NH2  yields  C6H2C13.NH2 
but  I  :  3  C6H4C1  .  NH2  yields  C6HC14.  NH2 

and  i  :  3  C6H3C12.  NH2  yields  C6C15. 


Another  interesting  example  of  the  connection  we  are 
considering  is  furnished  by  the  lactones,  under  which  name 
are  included  several  compounds  obtained  by  removing  the 
elements  of  water  from  hydroxy-acids,  or  the  elements  of 
hydrobromic  acid  from  bromo-acids:  thus  hydroxycaproic  acid 
C6H10(OH)  .  CO2H  yields  the  lactone  C5H10CO2,  and  bromo- 
valeric  acid  C4H8Br  .  CO2H  the  lactone  C4H8CO2.  Researches 
by  Fittig2  and  others  shew  that  lactones  are  formed  only 
from  those  acids  in  the  molecules  of  which  two  OH  groups, 
or  a  halogen  atom  and  an  OH  group,  are  directly  connected 
with  atoms  of  carbon  which  are  themselves  connected  indi- 
rectly through  two  other  carbon  atoms;  thus,  an  acid  repre- 

sented by  the  formula  ^Y-CHBr  (or  OH)-CH2-C<°H 

does  not  form  a  lactone,  but  when  acted  on  by  water  and  bases 
tends  to  produce  an  unsaturated  acid  ;  on  the  other  hand  an 
acid  represented  by  the  formula 

X  -  CHBr  (or  OH)  -  CH2  -  CH2  -  C 

readily  forms  a  lactone  the  constitution  of  which  is  probably 
represented  by  the  formula  X  CH  -  CH2  -  CH2  -  C^°  . 
Reference  may  also  be  made  to  the  connection  between 

1  See  C.  Langer,  Ber.  15.  1061  and  1328. 

2  See  R.  Fittig,  Annakn,  200.  21:  208.  in;  also  J.  Bredt,  Ber.  13.   748; 
also  E.  Hjett,  Ber.  15.  629. 


§  82]  ATOMIC  AND   MOLECULAR  SYSTEMS.  169 

the  structure  of  the  defines  (CHH2J  and  that  of  the  additive 
compounds  obtained  from  them  by  the  action  of  HX(X  =  C\, 
OH  &c.);  and  this  connection  may  be  compared  with  that 
existing  between  the  structures  of  the  haloid  derivatives  of 
the  olefines  and  the  additive  compounds  obtained  by  the 
action  on  these  holoid  derivatives  of  HX1. 

82.  From  these  considerations  it  would  appear  that  the 
readiness  to  undergo  this  reaction  or  that,  or,  as  might  be 
said,  the  chemical  stability  of  a  molecule,  depends  largely 
on  the  balance  of  properties  of  parts  of  the  molecule,  such 
balance  being  itself  connected  with  the  nature  and  relative 
arrangements  of  these  parts.  Many  of  the  reactions  cited 
in  the  foregoing  paragraphs  (80  and  81)  may  serve  as 
illustrations  of  the  meaning  of  the  expression  'chemical 
'stability',  and  of  the  conception  of  a  dependence  between  this 
and  the  balance  of  functions  of  parts  of  the  molecule;  let 
one  more  illustration  suffice. 

The  conditions  under  which  an  atom  of  hydrogen  ap- 
parently fulfils  alcoholic  functions  have  been  already  sum- 
marised [pp.  165 — 166].  In  some  molecules  the  acid  and 
alcoholic  functions  of  the  hydrogen  atoms  seem  to  be  equally 
balanced,  so  that  for  some  purposes  the  compound  may  be 
classed  as  an  alcohol,  for  other  purposes  as  an  acid ;  thus,  when 
an  atom  of  hydrogen  in  the  benzene  molecule,  C6Ha,  is  replaced 
by  the  group  OH,  the  product — C6H5.OH — exhibits  many  of 
the  properties  of  an  acid  and  also  many  of  the  properties  of 
an  alcohol,  e.g.  a  hydrogen  atom  is  replaceable  by  metal  when 
the  compound  is  acted  on  by  alkali  metal  or  alkaline  hydrox- 
ide, but  not  when  it  is  acted  on  by  an  alkaline  carbonate2. 
By  replacing  three  hydrogen  atoms  in  the  phenol  molecule 
— (C6H5.OH) — by  NH2  and  NO2  groups,  compounds  are  ob- 
tained which  exhibit  both  basic  and  acid  properties,  e.g.  the 
molecule  C6H2.(NH2).(NO2)2.OH  combines  with  the  molecule 
HC1,  but  the  product  is  not  very  stable ;  the  same  molecule 
however  readily  exchanges  an  atom  of  hydrogen  for  metal  by 

1  See  Armstrong  and  Groves,  loc.  cit.  pp.  181  and  200. 

2  In  these  actions  phenol  presents  an  analogy  to  aluminium  hydroxide — 

A12(OH)6. 


I/O  CHEMICAL   STATICS.  [§  83 

the  action  of  alkaline  carbonates,  thus  forming  well  marked 
stable  metallic  derivatives— e.g.  C6H2(NH2)(NO2)2ONa. 

If  however  two  NH2  groups  and  one  NO2  group  are 
introduced  in  place  of  three  hydrogen 'atoms  in  the  phenol 
molecule,  the  product  C6H2(NH2)2(NO2)OH  is  distinctly  basic, 
combining  readily  with  HC1,  but  yielding  only  unstable 
metallic  derivatives. 

83.  Not  only  is  the  general  chemical  stability  of  a 
molecule  dependent,  in  part,  on  the  balance  of  functions  of 
the  atoms  and  atomic  groups  in  the  molecule,  but  many  of 
the  properties  generally  called  physical  are  correlated  with  a 
similar  balance  of  parts.  Thus  Witt1  has  shewn  that  there 
exists  a  definite  connection  between  the  tinctorial  properties 
of  many  derivatives  of  azobenzene  (C6H5  — N2— C6H5)  and  the 
atomic  composition  and  structure  of  these  molecules.  By 
introducing  the  group  NH2  in  place  of  hydrogen  in  the  azo- 
benzene molecule,  salt-forming  molecules  are  produced, 
possessed  of  considerable  dyeing  properties ;  if  negative  groups, 
as  OH,  HSO3,  &c.  are  introduced  into  the  molecule  the 
products  are  also  strongly  coloured,  but  the  best  dyes  are 
formed  by  the  introduction  of  both  basic  and  acid  groups. 
Thus  C6H5-N2-C6H4(NH2)  dyes  a  light  yellow  but  the 
colour  is  very  fugitive;  the  colour  of 

(NH2)C6H4-N2-C6H3(NH2)2 

is  too  dull ;  but  C6H6  -  N2  -  C6H3(NH2)2.  HC1  acts  as  a  beautiful 
reddish  dye;  the  compound  whose  composition  is  represented 
by  the  formula  (NH.C6H5)C6H4-N2-C6H4(SO3H)  also  forms 
an  extremely  good  dye,  in  this  molecule,  the  basic  and  acid 
functions  are  nearly  balanced. 

We  have  already  learned  (pars.  32 — 35)  that  a  general 
relation  exists  between  the  crystalline  form  of  a  compound 
and  the  number  and  arrangement  of  the  atoms  in  the  molecule 
of  that  compound.  Groth2,  and  others,  have  shewn  that  the 

1  C.  S.  Journal  Trans,  for  1879.    179,  357. 

2  P°SS-    -Ann.    141.    31.      See    also     C.    Hintze,    Pogg.    Ergzbd.    6.    195; 
C.  Bodewig,  Pogg.  Ann.  158.   239;   P.  Friedlander,  Zeitschr.  Krystall,  3.  168; 
and  the  article  '  Isomorphie '  in  the  Neues  Handwbrterbuch  der  Chemie^  3.  espe- 
cially pp.  854—9. 


§83]  ATOMIC  AND   MOLECULAR   SYSTEMS.  i;i 

substitution  of  Cl,  Br,  NO2,  or  OH  &c.,  for  hydrogen  in  the 
molecule  of  benzene  derivatives  is  accompanied  by  definite 
changes  in  the  crystalline  forms  of  the  compounds.  The 
relations  existing  between  crystalline  form  and  chemical 
structure,  so  far  as  the  latter  is  modified  by  processes  of 
substitution,  are  called  by  Groth  morphotropic  relations.  The 
change  of  crystalline  form  in  any  given  case  depends  on 
(i)  the  chemical  nature  of  the  parent  substance,  (2)  the 
crystalline  system  to  which  it  belongs,  (3)  the  chemical  nature 
of  the  substituting  atom  (or  group)  and  (4)  the  chemical 
nature  of  the  product  of  the  reaction,  using  the  expression 
'chemical  nature'  in  its  widest  sense  as  including  the  con- 
ceptions of  atomic  composition  and  atomic  structure. 

When  the  parent  substance  belongs  to  a  crystalline  system 
in  which  the  relations  of  the  axes  are  not  invariable,  substitu- 
tion of  Cl,  Br,  &c.,  generally  only  produces  changes  in  these 
relations,  without  total  changes  to  other  systems;  but  if  the 
parent  substance  belongs  to  the  regular  system,  the  substituted 
product  is  found  to  belong  to  one  of  the  other  five  systems. 

Groth's  researches  lead  to  the  following  generalisations 
concerning  the  derivatives  of  benzene : — 

(1)  Substitution  of  H  by  OH,  or  NO2  is  accompanied 
by  changes  in  the  relations  of  the  axes,  but  not  by  changes 
from  one  system  to  another. 

(2)  Substitution  of  H  by  Cl  or  Br,  is  accompanied  by 
changes  from  one  crystalline  system  to  another,  less  sym- 
metrical, system ;  but  further  substitution  of  the  same  atoms  is 
sometimes  accompanied  by  a  return  to  a  more  symmetrical 
system. 

(3)  Substitution  of  H  by  CH3  is  also  accompanied  by 
marked  changes  in  crystalline  symmetry. 

Chemically  similar  derivatives  of  benzene  belonging  to  a 
para  [1:4]  series  shew  greater  crystallographic  analogy  with 
one  another  than  with  the  members  of  a  meta  [i  :  3]  or  an  ortho 
[1:2]  series.  This  statement,  when  rendered  more  definite  by 
extended  investigations,  will  doubtless  lead  to  important  gene- 
ralisations connecting  crystalline  form  with  atomic  arrange- 
ment ;  meanwhile  it  may  be  tentatively  applied  in  some  of 


1 72  CHEMICAL  STATICS.  [§84 

the  problems  presented  by  isomorphism.  Thus,  I  :  3  dinitro- 
benzene  on  nitration  yields  a  certain  trinitrobenzene;  to  which 
of  the  three  series  of  benzene-derivatives  does  this  trinitro-com- 
pound  belong1?  If  the  formulae  of  the  possible  trinitrobenzenes 
are  compared  with  those  of  the  three  dinitrobenzenes  it  will  be 
found  that  I  :  2  dinitro-  can  yield  2  trinitrobenzenes,  (viz. 
1:2:3,  and  I  :  3  : 4),  i  :  3  dinitro-  can  yield  3  trinitrobenzenes, 
(viz.  1:2:3,  1:3:4,  and  1:3:5),  and  1:4  dinitro-  can  yield 
only  one  trinitrobenzene  (viz.  1:3:4.)  Of  the  three  possible 
trinitrobenzenes,  the  1:3:4  is  obtainable  from  each  of  the 
three  dinitro-compounds,  the  1:2:3  'ls  obtainable  from  either 
the  I  :  2  or  the  I  :  3  dinitro-compound,  but  the  1:3:5  is 
obtainable  from  the  1 : 3  dinitro-compound  only. 

Now  let  us  distinguish  the  crystalline  form  of  the  trinitro- 
benzene, a  formula  for  which  is  to  be  found,  by  the  symbol  D. 
The  compound  in  question  is  obtained  from  the  I  :  3  dinitro- 
benzene ;  if  it  is  the  1:3:4  compound,  then  a  trinitrobenzene 
having  the  symbol  D  should  be  obtained  from  each  of  the 
other  dinitrobenzenes,  if  it  is  the  1:2:3  compound,  then  a 
trinitrobenzene  having  the  symbol  D  should  be  obtained  from 
I  :  2  but  not  from  I  :  4  dinitrobenzene.  But  experiment  shews 
that  one  and  only  one  trinitrobenzene,  the  crystalline  form 
of  which  we  have  designated  by  D,  is  obtainable ;  hence  the 
conclusion  is  that  the  compound  in  question  is  1:3:5  trinitro- 
benzene. 

The  general  conclusion  to  be  drawn  from  these  facts  is, 
that,  in  some  compounds  at  any  rate,  crystalline  form  is 
more  or  less  closely  connected  with  the  nature  and  arrange- 
ment of  the  atoms  and  groups  of  atoms  in  the  compound 
molecules. 

84.  Very  many  measurements  have  been  made  of  the  quan- 
tities of  heat  evolved  or  absorbed  during  processes  of  chemical 
change :  this  subject  will  be  considered  in  detail  in  a  future 
chapter  ;  at  present  I  wish  to  insist  on  the  fact  that  the  data  of 
thermal  chemistry  establish  an  undoubted  connection  between, 
the  thermal  changes  which  accompany  chemical  reactions 
and  the  nature  and  arrangement  of  the  atoms,  and  groups  of 

1  See  '  Isomorphie,'  !oc.  cit.  p.  858. 


§  84]  ATOMIC  AND   MOLECULAR  SYSTEMS.  173 

atoms,  in  the  molecules  which  take  part  in  these  reactions. 
Especial  reference  must  here  be  made  to  the  experiments  of 
J.  Thomsen1,  from  which  that  naturalist  has  drawn  the  con- 
clusion that  it  is  possible  to  assign  a  definite  thermal  value 
to  the  atomic  transaction  expressed  in  the  language  of  the 
theory  of  valency  as  '  change  from  acting  as  a  divalent  to 
'acting  as  a  trivalent  carbon  atom/  or  'from  acting  as  a 
'trivalent  to  acting  as  a  tetravalent  carbon  atom.'  Thus, 
representing  the  changes 

(i)  C2H2  +  H2=C2H4,        (2}  C2H4  +  H2=C2H6 
in  structural  formulae  we  have 

(i)  H^  ^H 

H  — C  — C  — H  +  H  — H  =     ^C  — C^     ; 

H  H 

-        <2)HN  ^  H      H  '     IH 

C  — C        +  H  — H  =  H  — C— C  — H. 

/  \  II 

H      H 

Now  Thomsen  seeks  to  separate  the  thermal  change 
accompanying  the  addition  of  H2  to  C2H2,  or  to  C2H4,  from 
that  which  he  supposes  to  accompany  the  change  of  divalent 
into  trivalent,  or  trivalent  into  tetravalent  carbon  atoms. 
Thomsen  does  not  himself  put  the  statement  of  what  he 
wishes  to  do  in  this  form  ;  he  uses  the  language  of  the  theory 
of  bonds;  he  calculates  the  'heats  of  formation2'  of  C2H2, 
C2H4,  and  C2H6,  i.e.  of  hydrocarbon  molecules  containing  (i) 
a  pair  of  'trebly-linked'  carbon  atoms,  (2)  a  pair  of 'doubly- 
'  linked,'  and  (3)  a  pair  of  'singly-linked'  carbon  atoms3.  By 

1  Ber.  13.  1321,  and  Journal  fur  prakt.  Chemie.  23.  157  and  163.     See  also 
post.  chap.  IV.,  par.  134. 

2  '  Heat   of  formation '   of  a   compound  =  difference   between  heat  evolved 
during  complete  combustion  of  the  elementary  constituents  of  the  compound, 
and  heat  evolved,  during  complete  combustion  of  the  compound  itself,  stated  in 
thermal  units  per  formula-weight  of  the  compound.     (See  chapter  IV. ,  par.  120.) 

3  The  bond  theory  represents  the  molecules  in  question  thus: 

(i)    H-CEC-H,        (2)    H2=C  =  C  =  H2,        (3)    H3=C-C  =  H3. 


1/4  CHEMICAL  STATICS.  [§  84 

making  many  assumptions,  concerning  the  structure  of  the 
molecule  of  carbon,  and  the  amounts  of  heat  absorbed  in 
separating  carbon  and  hydrogen  molecules  into  atoms,  &c., 
Thomsen  deduces  certain  thermal  values  for  the  *  satisfaction 
*  of  each  bond,'  or  affinity,  of  the  carbon  atom  by  a  bond,  or 
affinity,  of  another  carbon  atom.  The  thermal  values  thus 
obtained  differ,  according  to  Thomsen,  for  each  bond ;  in 
other  words  the  quantity  of  heat  evolved  during  the-  satisfac^ 
tion  of  bond  a  is  different  from  that  evolved  during  the  satis- 
faction of  bond  b,  which  quantity  again  is  not  the  same  as 
that  accompanying  the  satisfaction  of  bond  c.  Or  we  may 
put  the  matter  thus, — the  thermal  value  of  the  theoretically 
occurring  transaction 

-C— +— C— =  XC-,c" 

I  I 

is  not  double  the  value  of  the  other  transaction 

i  I 

—  c— +  — c— =  — c  — c— , 

I         I 

nor  is  the  latter  of  these  represented  by  one-third  of  the 
thermal  value  of  the  transaction 

I  I 

—  c—  +  —  c—  =  —  c=.c— . 

I         I 

Indeed  Thomsen  arrives  at  the  conclusion,  strange  when 
stated  in  the  language  of  the  bond  theory,  that  '  the  treble- 
'  linking  of  two  atoms  of  carbon  is  accompanied  by  no 
'  thermal  change.' 

It  seems  to  me  that  Thomsen's  conclusions,  when  stated 
in  the  terminology  of  the  theory  of  bonds  oblige  one  to  say 
either  that  this  theory  is  meaningless,  or  that  Thomsen's 
results  are  absurd;  for,  a  'bond'  is  a  'unit  of  affinity,'  it 
is  something  that  can  be  'satisfied,'  when  one  bond  of  a 
carbon  atom  is  satisfied  by  one  bond  of  another  carbon 
atom  the  loss  of  energy  by  the  system  is  measured  (ac- 


§§85,86]        ATOMIC  AND    MOLECULAR   SYSTEMS.  175 

cording  to  Thomsen)  by  about  15,000  gram- units  of  heat,  but 
when  three  bonds  of  a  carbon  atom  are  satisfied  by  three 
bonds  of  another  carbon  atom  the  loss  of  energy  by  the 
system  is  equal  to  zero. 

85.  But    if  we   regard    Thomsen's   results   as   teaching, 
in  a  general  way,  that  the  change  from  a  material  system 
of  isolated  atoms — say  x  carbon  atoms,  x  hydrogen  atoms, 
and  x"    oxygen  atoms — to   a    molecular    system   in   which 
these   atoms    are   combined    so   that   all   the   carbon    atoms 
are  tetravalent  (i.e.  each  acts  on  and  is  acted    on   by   four 
other  atoms)  and  all  the  oxygen  atoms  are  divalent,  is  at- 
tended   with    the    loss   of    a   quantity    of    energy   different 
from   that   which   accompanies  the  change   from  the   same 
system  of  isolated  atoms  to  a  molecular  system  in  which 
some — say   (x  -  2) — carbon  atoms    are    trivalent,   and   some 
— say  (x—i) — oxygen  atoms  are  monovalent ;    if  we  regard 
this,   or  something  like  this,   as  the  general    lesson    taught 
by  Thomsen's  results,  then  I   think  these   results  must  be 
regarded  as  marking  an  advance  in  the  conception  of  mole- 
cular structure. 

86.  But  few  measurements  have  yet  been  made  of  quan- 
tities of  heat  absorbed  or  evolved  during  similar  chemical 
changes  undergone  by  isomeric  compounds,  but  those  which 
have  been  made — e.g.  heats  of  oxidation  of  benzene  and  its 
isomeride  dipropargyl— seem    to    shew  that   in  many  cases 
at  any  rate  the  quantity  of  energy  associated  with  one  iso- 
meride is  different  from  that  associated  with  another.     Thus, 
the  heat  evolved  during  the  complete  combustion  of  dipro- 
pargyl (C6H6)  is  about  850,000  gram-units,  while  that  evolved 
during  the  combustion  of  the  isomeric  molecule  benzene  is 
about    800,000    gramrunits ;     hence   the   amount   of  energy 
associated  with  the  arrangement  of  six  atoms  of  carbon  and 
six  atoms  of  hydrogen  in  the  molecule  of  benzene  is  less,  by 
about  50,000  thermal  gram-units,  than  that  associated  with 
the  arrangement  of  the  same  numbers  of  the  same  atoms 
in  the   molecule   of  dipropargyl.      But   in   the   molecule   of 
benzene  each  carbon  atom  is  at  least  trivalent  (and  possibly 
tetravalent),  while  in  that  of  dipropargyl  some  of  the  carbon 


176  CHEMICAL  STATICS.  [§  86 

atoms  are  certainly  divalent1 ;  hence,  it  might  apparently  be 
concluded,  that  more  energy  is  lost  in  the  formation,  from 
atoms  of  carbon  and  hydrogen,  of  a  molecule  in  which  all 
the  carbon  atoms  act  as  tri-  or  tetravalent  atoms,  than  of  an 
isomeric  molecule  in  which  some  of  the  carbons  act  as  diva- 
lent atoms.  But  it  must  be  remembered  that  in  the  benzene 
molecule  each  carbon  atom  acts  on,  and  is  acted  on  by,  not 
more  than  one  atom  of  hydrogen,  and  on  at  least  two  other 
atoms  of  carbon,  whereas  in  the  molecule  of  dipropargyl  it 
is  very  probable  that  two  of  the  carbon  atoms  act  each  on  a 
single  other  carbon  atom,  and  also  that  some  of  the  atoms 
of  carbon  act  each  on  two  atoms  of  hydrogen.  Hence,  it 
we  may  provisionally  draw  a  general  conclusion  from  the 
limited  data  before  us,  it  might  be  inferred  that  the  differences 
between  the  quantities  of  energy  associated  with  different 
atomic  systems  depend,  among  other  conditions,  on 

(1)  whether  each  atom  acts  on,  and  is  acted  on  by,  the 

maximum  number  of  other  atoms  which  can  come 
within  its  binding-sphere ;  in  other  words,  on  the 
actual  valencies  of  the  atoms  in  the  molecules ; 
and 

(2)  on  the  nature  of  the  atoms   between  which  direct 

mutual  action  occurs. 

1  If  Kekule's  formula  (i)  for  benzene  is  adopted  each  carbon  atom  is  trivalent; 
if  Ladenburg's  formula  (2)  is  adopted  each  carbon  atom  is  tetravalent  j 
H 

I  H 

C  C 


/  \ 

H— C     C— H  HC- 

(i)  II-.  (*) 

H— C     C— H  HC- 


-CH 
-CH 


I  H 

H 

the  usually  adopted  formula  for  the  dipropargyl  molecule  is 

H    H 
I       I 

H— C— C— C— C— C— C— H 
I      I 
H    H 

which  contains  2  tetra-  and  4  divalent  carbon  atoms. 


§§  8/,  88]        ATOMIC   AND   MOLECULAR   SYSTEMS. 


177 


87.  The  following  data,  in  addition  to  the  numbers  given 
for  the  heats  of  combustion  of  benzene  and  dipropargyl, 
serve  to  illustrate  the  existence  of  a  relation  between  the 
quantities  of  energy  in  molecules  and  the  valencies  of  the 
atoms  which  form  these  molecules. 


Empirical  formula 


(i)  propaldehyde,        H 

I          X0 
H3C-C-C 


Heat  of  combustion. 


420,000  gram- 
units  + . 


H 


(2)  allylalcohol, 


H2 

II 


H2= C  —  C  —  C  —  O  —  H     442,000  gram- 
|  units  -f- . 

H 

Assuming  the  correctness  of  these  structural  formulae,  it 
is  seen  that  the  propaldehyde  molecule  contains  two  tetra- 
and  one  trivalent  carbon  atoms,  and  also  one  monovalent 
oxygen  atom,  whereas  the  molecule  of  allylic  alchohol  con- 
tains two  tri-  and  one  tetravalent  carbon  atoms,  and  also  one 
divalent  oxygen  atom. 

88.  The  data  of  thermal  chemistry  furnish  more  numer- 
ous examples  of  the  existence  of  a  connection  between 
greater  or  less  molecular  energy  and  the  distribution  of  the 
mutual  atomic  actions  within  isomeric  molecules. 

Thus, 

Heat  of  combustion. 

/(i)  ethyl  formate, 


Empirical  formula 
C3H602 


H 
I 
H  — C  — O  — C  — C  =  H3 

I  I 

O  H 

(2)  methyl  acetate, 

H3=C-C-0-C=H3 

O 


390,000  gram- 
units +  . 


395,000  gram- 
units +. 


If  the  structural  formulae  given  are  correct,  then  in  each 

of  these    molecules  we   have   two   tetra-  and   one   trivalent 

carbon   atoms,   and   one   mono-   and   one    divalent    oxygen 

atoms ;  but  the  trivalent  carbon  atom  in  ethyl  formate  acts 

M.  C.  12 


1 73  CHEMICAL   STATICS.  [§  89 

directly  on  two  oxygen  and  one  hydrogen  atoms,  and  in 
methyl  acetate  on  two  oxygen  and  one  carbon  atoms  :  in- 
spection of  the  formulae  will  disclose  other  differences  in  the 
distribution  of  the  atomic  interactions. 

Alcohol  and  methylic  oxide  afford  another  example  of  the 
relation  we  are  discussing ; 

Heat  of  combustion. 

f(i)  alcohol,  H 

=  C  —  C  —  O  —  H     330,000  gram- 
Empirical  formula  J        .  units +  . 
QHfiO 

(2)  methylic  oxide, 

H3IEC  —  O  —  C  =  H3        344,000  gram-units +  . 

We  have  here  two  molecules  each  containing  a  pair  of  tetra- 
valent  carbon  atoms,  one  divalent  oxygen,  and  six  mono- 
valent  hydrogen  atoms,  but  in  one  of  the  molecules  each 
carbon  atom  acts  on  three  hydrogen  and  one  oxygen  atoms, 
while  in  the  other  the  arrangement  of  atomic  interactions 
is  less  symmetrical. 

Another  example  is  afforded  by  the  three  hydroxybenzoic 
acids ; 

Heat  of  combustion. 

(i)     1:4  hydroxybenzoic  acid, 

C6H4(OH)CO2H     75  2,000  gram-units +  . 


Empirical  formula 
C7H603 


(2)  1:3        »  »         7543ooo    „        „     +. 

(3)  1  =  2        „  „         759,ooo    „        „     +. 


89.  The  data  are  not  sufficient  to  warrant  any  precise 
statement  as  to  the  relations  between  quantities  of  energy 
and  molecular  structure.  It  is  possible  that  the  case  of 
benzene  and  dipropargyl  is  typical,  and  that  of  two  isomeric 
molecules,  one  of  which  belongs  to  the  class  of  ring-formed 
and  the  other  to  that  of  open-chain  molecules,  the  former 
always  contains  relatively  less  energy  than  the  latter.  It  is 
also  possible  that  of  two  isomeric  carbon  compounds,  the 
molecules  of  which  belong  to  the  open-chain  class,  and  in 
which  rt±  <  2;z4  +  . . .  2,  that  containing  the  greater  number  of 


§  89]  ATOMIC  AND   MOLECULAR   SYSTEMS.  179 

tetravalent  carbon  atoms  contains  the  smaller  quantity  of 
energy,  provided  that  the  distribution  of  the  atomic  inter- 
actions is  the  same,  or  nearly  the  same,  in  the  two  molecules. 
Or  again  it  may  be  that  when  the  actual  valencies  of  the 
atoms  in  two  or  more  isomeric  molecules  are  the  same,  that 
molecule  in  which  the  atomic  interactions  are  distributed  so 
as  to  produce  the  greatest  degree  of  symmetry  is  marked  by 
the  smallest  amount  of  energy1.  But  we  have  as  yet  no 
accurate  knowledge  which  may  enable  us  to  test  the  applica- 
bility of  these  suggestions. 

Even  if  it  could  be  asserted  (as  seems  possible  in  a  few 
cases)  that  this  isomeride  contains  relatively  less  energy  than 
that,  and  is  therefore  more  stable,  the  question  would  arise, 
what  do  we  mean  by  stability  ?  For  although  of  two  mole- 
cules, a  may  be  the  more  stable,  as  stability  is  measured  by 
thermal  changes,  it  may  nevertheless  be  impossible  to  say 
that  a  is  possessed  of  greater  chemical  stability  than  b.  But  a 
discussion  of  the  meaning  and  application  of  the  expression 
chemical  stability,  requiring  as  it  does  a  knowledge  of  the 
facts  and  theories  of  chemical  affinity,  will  find  a  fitter  place 
in  that  part  of  this  book  which  deals  with  chemical  kinetics. 

Inasmuch  as  variations  in  the  physical  properties  of  ma- 
terial systems  accompany  variations  in  the  energies  of  these 
systems,  it  follows  (if  the  two  very  general  assumptions  made 
on  p.  176  concerning  the  connection  between  energy  and 
structure  of  isomeric  molecules  are  granted)  that  physical 
phenomena,  other  than  thermal,  may  be  expected  to  exhibit 
variations  in  isomeric  molecules. 

An  attempt  will  be  made  in  a  future  chapter  to  summarise 
the  more  important  physical  phenomena,  between  which  and 
molecular  structure  in  general  there  is  an  established  con- 
nection. Here  I  would  only  remark  that  the  researches  of 
various  chemists  on  the  '  specific  volumes '  of  liquid  com- 
pounds, seem  to  shew,  that  the  influence  of  any  atom  on  the 
'  specific  volume '  of  a  compound  molecule  is  dependent,  not 

1  This  view  is  put  forward  tentatively  by  Carnelley,  Phil.  Mag.  [5]  13.  1 80. 
[In  this  paper  will  be  found  most  of  the  thermal  data  bearing  on  the  subject  of  the 
stability  of  isomeric  molecules.] 

12 — 2 


180  CHEMICAL   STATICS.  [§  90 

only  on  the  nature  and  on  the  actual  valency  of  that  atom, 
but  also  on  the  nature  of  the  other  atom,  or  atoms,  between 
which  and  the  given  atom  there  is  direct  action  and  reaction. 
On  the  other  hand,  the  work  of  Briihl  has  rendered  it  probable, 
that,  in  isomeric  carbon  compounds,  the  influence  exerted  by 
a  polyvalent  atom  on  the  '  molecular  refraction '  is  to  a  large 
extent  dependent  on  the  actual  valency  of  that  atom,  i.e.  on 
the  number,  rather  than  on  the  nature,  of  other  atoms  on 
which  it  acts  directly1. 

90.  Much  is  to  be  expected  from  researches  into  the 
phenomena  which  occupy  the  border-land  between  chemistry 
and  physics.  If  the  knowledge  chemists  already  have  of  the 
structure  of  molecules,  meagre  though  that  knowledge  be,  can 
be  supplemented  by  definite  dynamical' conceptions,  obtain- 
able in  part  by  the  methods  of  thermal  chemistry,  then  we 
may  hope  that  chemistry  will  enter  on  a  new  stage  of  advance 
as  a  branch  of  the  science  of  matter  and  motion.  It  seems  to 
me  that  a  most  important  step  will  be  made  if  the  bond 
theory  of  valency  is  generally  abandoned  ;  with  it  will  go  all 
those  quasi-dynamical  expressions,  the  offspring  of  loose  and 
slipshod  ways  of  thinking,  which  have  gathered  round  that 
strange  anomaly,  a  '  unit  of  affinity,'  employed  as  a  variable 
standard  for  measuring  nothing. 

Jf  it  be  decided  that  by  the  valency  of  an  atom  is  meant 
the  maximum  number  of  other  atoms  between  which  and  the 
given  atom  there  is,  so  far  as  we  know,  direct  action  and 
reaction  in  any  molecule,  then  we  are  put  in  possession  of 
a  definite  conception  which  may  be  applied  to  actually  oc- 
curring phenomena,  and  the  application  of  which  will  gradu- 
ally lead  to  more  precise  knowledge  regarding  the  distribu- 
tion of  the  atomic  interactions  in  various  molecules.  But  at  the 
same  time  that  we  are  classifying  molecules  in  accordance  with 
the  valencies  of  their  constituent  atoms  and  the  distribution 
of  the  mutual  actions  of  these  atoms,  in  a  word,  in  accordance 
with  their  structure,  we  are  also  becoming  more  impressed 
with  the  inadequacy  of  this  classification  ;  we  see  a  vast  field 

1  Seefost,  chap.  iv.  par.  139. 


§  Ql]  ATOMIC   AND   MOLECULAR   SYSTEMS.  l8l 

opening  for  investigation,  we  see  that  measurements  of  losses 
or  gains  of  energy  are  required,  and  that  determinations  of 
many  physical  constants  are  called  for.  We  begin,  I  think, 
to  perceive  that  this  knowledge,  when  gained,  will  supplement 
and  not  supplant  that  which  is  already  possessed  by  us,  and 
that  it  will  do  this  by  leading  to  an  exact  knowledge  of  the 
way  in  which  the  variations  in  the  energies  of  molecules  are 
connected  with  changes  in  the  configuration  and  motion  of 
the  atoms  which  constitute  these  molecules. 

91.  Admitting  that  the  definition  of  valency  given  by 
Lossen  furnishes  a  better  working  hypothesis  than  any  other, 
it  becomes  necessary  to  inquire  whether  this  definition  and 
the  conceptions  which  arise  from  it  can  be  applied  to  all 
known  cases  of  isomerism. 

In  the  article  ISOMERISM,  by  Dr  Armstrong,  in  Watts's 
Dictionary,  supplt.  III.,  will  be  found  an  account  of  most  of 
those  compounds  which  are  regarded  as  presenting  phe- 
nomena inexplicable  in  terms  of  the  usually  adopted  theory 
of  isomerism. 

If  the  facts  in  this  article  are  classified,  it  will,  I  think,  be 
apparent  (i)  that  structural  formulae  in  keeping  with  reac- 
tions may  be  assigned  to  some  of  the  isomeric  compounds 
mentioned — e.g.  to  the  acrylic  acids,  to  maleic  and  fumaric 
acid,  and  to  the  acids  obtained  by  heating  citric  acid — provided 
we  cease  to  regard  the  conventional  method  of  expressing 
valency  by  one  or  more  straight  lines,  as  affording  any  quan- 
titative measurements,  even  relative  measurements,  of  atomic 
interactions ;  (2)  that  other  cases  of  unexplained  isomerism  — 
e.g.  the  dinitrochlorobenzenes,  the  nitrotetrabromobenzenes, 
and  probably  many  of  the  terpenes1 — are  almost  certainly 
illustrations  of  modifications  in  properties  being  correlated 
with  variations  in  mutual  actions  between  groups  of  molecules 
rather  than  between  the  atoms  constituting  each  molecule ; 
and  (3)  that  the  remaining  cases  are  true  residual  phenomena, 

1  That  optical  properties  are  not  always  dependent  on  the  structure  of  the 
molecule  is  shewn  by  the  ease  with  which  optically  active  amylic  alcohol  and 
valeric  acid  are  converted  into  the  inactive  alcohol,  and  acid,  without  change  of 
chemical  properties.  See  Armstrong  and  Groves,  loc.  cit.  p.  449. 


1 82  CHEMICAL  STATICS.  [§91 

at  present  inexplicable  in  terms  of  the  prevailing  theory  but 
not  therefore  contradictory  of  that  theory. 

The  theory  of  valency  can  only  be  applied  to  the  mole- 
cules of  gases  :  if  this  is  remembered  the  so-called  exceptional 
cases  of  isomerism  appear  no  longer  exceptional,  they  are 
simply  assertions  of  the  fact  that  our  theory  is  partial. 

Among  the  more  important  apparently  inexplicable  phe- 
nomena of  isomerism  are  those  presented  by  the  terpenes, 
hydrobenzoin,  dulcitol,  the  lactic  and  the  tartaric  acids,  and 
the  acids  obtained  by  Perkin  from  coumarin1. 

Chemists  are  quite  undecided  as  to  the  structural  formula 
to  be  assigned  to  any  molecule  the  composition  of  which  is 
represented  by  the  empirical  formula  C10H16 ;  there  is  no  need 
to  bring  within  the  theory  hypothetical  molecules  which  per- 
haps have  no  existence.  We  do  not  certainly  know  the  mole- 
cular weights  of  hydrobenzoin  and  isohydrobenzoin ;  but 
assuming  the  generally  employed  formulae  to  be  molecular, 
it  seems  necessary  to  suppose  that  the  molecule  of  one  of 
these  compounds  contains  two  OH  groups  in  direct  combina- 
tion with  the  same  atom  of  carbon  :  our  actual  knowledge  of 
the  connections  between  molecular  structure  and  stability  is 
not  advanced  sufficiently  for  us  to  deny  the  possibility, 
although  we  may  assert  the  improbability,  of  such  a  formula2. 
We  know  too  little  of  the  reactions  of  mannitol  and  dul- 
citol to  enable  us  to  decide  between  the  possible  structu- 
ral formulae  of  these  compounds.  Lactic  and  sarcolactic 
acids  are  extremely  unstable ;  even  in  aqueous  solutions  they 
readily  undergo  changes  ;  intermolecular  actions  are  probably 
frequently  occurring  in  any  mass  of  either  of  these  com- 
pounds. Tartaric  and  laevotartaric  acids  may  have  different 
molecular  weights;  the  differences  in  physical  properties  which 
they  exhibit  are  differences  between  solids,  and  we  know 
almost  nothing  of  the  laws  regulating  molecular  phenomena 
in  liquid  and  solid  bodies.  Perkin3  has  described  two  series 

1  See  the  article  by  Armstrong,  loc.  cit. 

2  It  seems  however  very  probable  that  these  two  compounds  belong  to  the  class 
of  ' physically  isomeric'  bodies;  see  Zincke,  Annalen  198.  191. 

3  C.  S.  Journal.  Trans,  for  1881.  409. 


§92]  ATOMIC   AND   MOLECULAR   SYSTEMS.  183 

of  acids  derived  from  coumarin,  having  the  same  elementary 
composition  but  differing  in  physical  properties ;  any  one 
acid  is  generally  changeable  into  its  isomeride  by  the  action 
of  heat,  the  process  being  in  many  cases  reversible  by  the 
same  agency.  But  these  changes  are  accompanied  by  pro- 
cesses of  hydration  and  dehydration,  and  would  appear  to 
consist  in  great  part  of  intermolecular  actions,  and  not  only 
in  interactions  of  the  atoms  constituting  the  molecules.  But 
of  intermolecular  actions  we  know  as  yet  very  little. 

92.  The  properties  of  any  mass  of  a  solid  or  liquid  com- 
pound seem  to  be  conditioned,  not  only  by  the  valencies  of 
the  atoms  which  constitute  the  molecule  of  that  compound, 
by  the  distribution  of  the  atomic  actions  within  the  molecule, 
and  by  the  relatively  large  or  small  quantity  of  energy  asso- 
ciated with  this  atomic  configuration,  but  also  by  actions  and 
reactions  between  groups  of  molecules,  the  parts  of  which 
groups  hold  together  during  more  or  less  wide  variations  in 
the  physical  conditions  to  which  the  compound  may  be 
subjected1. 

The  hypothesis  that  groups  of  molecules,  marked  by  fairly 
definite  properties,  may  exist,  and  may  mutually  act  and 
react,  enables  us  to  give  a  partial  explanation  of  various  facts 
concerning  liquid  and  solid  compounds  which  cannot,  ap- 
parently, be  so  well  explained  by  any  other  molecular  hy- 
pothesis that  has  been  suggested. 

The  phenomena  presented  by  calcium  carbonate  are  typical 
of  those  to  be  explained  by  the  help  of  the  hypothesis  in 
question.  Calcspar  and  arragonite  are  composed  of  calcium, 
carbon  and  oxygen  united  in  the  proportions  expressed  by 
the  formula  CaCO3 ;  arragonite  crystallises  in  rhombic  forms, 

1  According  to  Henry  \Ber.  4.  604],  the  two  chlorobromopropanes, 

H  H 

I  I 

H3C— C— CH2C1  and    H3C— C— CH2Br, 

Br  Cl 

are  identical  in  physical  properties :  if  this  is  really  so,  we  have  an  instance  of 
identity  of  physical  properties  accompanied  by  a  slight  difference  in  the  distribu- 
tion of  atomic  interactions  within  the  molecule. 


1 84  CHEMICAL   STATICS.  [§92 

calcspar  in  hexagonal  forms  ;  arragonite  is  harder,  and  speci- 
fically heavier  than  calcspar,  nor  is  it  so  easily  acted  on  by 
various  reagents,  e.g.  hydrochloric  or  acetic  acid,  or  ammo- 
nium chloride  or  nitrate  ;  when  powdered  arragonite  is  heated 
to  redness  it  is  changed  into  calcspar,  but  the  reverse  change 
is  not  accomplished  by  the  same  agency ;  both  modifications 
of  calcium  carbonate  can  be  produced  at  low  temperatures, 
but  there  is  a  certain  temperature  above  which  only  calcspar  is 
formed.     Calcspar   and  arragonite   thus    exhibit   identity  of 
elementary  composition  (perhaps  the  same  molecular  weight) 
accompanied  by  differences  of  physical,  and  to  some  extent  of 
chemical  properties.     Another  typical  instance  is  afforded  by 
antimonious  iodide,  SbI3;  this  compound  crystallises  in  red- 
coloured  hexagonal  forms,  which  when  heated  to  1 14°  are  sud- 
denly changed  into  a  mass  of  yellow-coloured  orthorhombic 
crystals,  the  original  external  form  of  the  mass  being  however 
preserved1.      Several  carbon  compounds  (apparently  all   be- 
longing to  the  class  of  benzenoid  compounds)  exist  in  more 
than  one  form,  each  modification   being  characterised   by  a 
definite  melting  point  and  generally  also  by  a  special  crystal- 
line form.    Thus  chlorodinitrobenzene — C6H3C1(NO2)2  [1:2:4] 
— is  said  to  form  monoclinic  crystals  which  melt  at  36°,  and 
also  rhombic  crystals  which  melt  at  39°.     Anthracene,  CUH10, 
crystallises  in    monoclinic  plates   melting  at  213°  which  are 
easily  oxidised  by  the  action  of  nitric  acid  to  anthraquinone 
(C14H8O2) ;   when   a   solution,  in    benzene,   of  anthracene   is 
exposed  to  sunlight  small  prismatic  crystals  separate,  melting 
at  244°,  having  the  composition  C14H10,  but  not  acted  on  by 
nitric  acid,  and  not  oxidised  to  anthraquinone  by  chromic 
acid2.     A  very  remarkable  instance  of  the  phenomenon  under 
consideration  is  presented  by  the  derivative  of  diphenyl  to 
which   the   formula  (C6H3BrNHCOC6H5)2  is  assigned.     This 
compound    melts  at   195°;   if  the  melted  substance  is  cooled 
quickly  and  again  heated  its  melting  point  is  now  99° ;  but  if 
heating  is  continued  the  liquid  again  solidifies  at  125—130°, 
and  the  solid  thus  obtained  melts  once  more  at  195°.     Finally 

1  J.  P.  Cooke,  Proc.  Amer.  Acad.  of  Arts  and  Sci.  [2]  5.  72. 

2  See  Armstrong  and  Groves,  loc.  cit.  p.  199. 


§93]  ATOMIC   AND   MOLECULAR   SYSTEMS.  185 

if  the  solid  which  melts  at  195°  is  raised  to  that  temperature 
and  then  slowly  cooled,  the  product  possesses  the  normal  melting 
point,  viz.  I951.  When  a  substance  crystallises  in  more  than 
one  system,  one  crystalline  form  approaches  as  nearly  as 
possible  to  the  other,  one  form  appears  to  imitate  the  other 
both  crystallographically  and  optically2 ;  thus  arsenious  oxide 
crystallises  in  regular  octahedra  and  also  in  rhombic  prisms, 
the  latter  exhibiting  an  angle  identical  with  the  angle  of  the 
regular  octahedron. 

93.  O.  Lehmann3  has  collected  and  discussed  many  in- 
stances of  the  exhibition  of  different  physical  properties  by 
compounds  possessing  the  same  elementary  composition4. 
The  phenomenon,  which  may  be  called  physical  isomerism*) 
presents  analogies  with  allotropy  (see  ante,  par.  67) ;  in  both, 
temperature  is  the  most  important  condition  affecting  the 
change  from  one  form  to  another,  and  this  change  is  ac- 
companied in  both  classes  of  phenomena  by  absorption  or 
evolution  of  heat. 

In  the  term  allotropy  are  summed  up  similar  phenomena 
which  appear  to  be  best  explained,  in  terms  of  the  molecular 
theory,  by  the  hypothesis  that  variations  in  the  numbers  of 
atoms,  all  of  one  kind,  constituting  a  molecule,  may  be  ac- 
companied by  variations  in  the  physical,  and  to  some  extent 
chemical  properties,  of  the  substance  which  is  composed  of 
these  molecules.  But  the  term  is  also  applied  to  phenomena — 
e.g.  the  variation  in  melting  points,  &c.  of  solid  sulphur — which 
are  probably  better  explained  by  the  hypothesis  that  what 
may  be  called  the  acting  physical  unit,  or  the  physical  mole- 
cule, of  each  allotropic  form  is  constituted  of  a  different 
number  of  chemical  molecules.  In  this  view  of  the 


//  0  '<•     ,        Jl 

1  See  E.  Lellmann,  Ber.  15.  2835.  (f^^"/  V  *F  1 

2  Pasteur,  Ann.  Chim.  Phys.  [3]  23.  267. 

3  Zeitschr.  fur  Krystallog.  1.   97.     See  also,   in  connection  with  the  subject 
generally,  the  article '  Isomerie,  physikalische'  in  Nettes  Handworterbiich  der  Chemie,. 
Bd.  in.  pp.  836 — 843. 

4  On  this  subject  see  also  Laubenheimer,  Ber.  9.  760. 

5  The  term  physical  isomerism  seems  to  have  been  first  used  by  L.  Carius, 
Annalen,  126.  214(566  also  do.  130.  237). 


1 86  CHEMICAL   STATICS.  [§94 

the  term  physical  isomerism  would  embrace  phenomena  com- 
mon to  elements  and  compounds. 

94.  Lehmann  (loc.  cit.)  divides  physically  isomeric  bodies 
into  two  classes  :  (i)  those  in  which  change  from  one  form  to 
another  occurs  at  a  definite  temperature,  the  direction  of  the 
change  being  dependent  on  very  small  differences  of  tem- 
perature ;  (2)  those  which  exhibit  two  forms,  one  more  stable 
than  the  other,  and  in  which  change  from  one  form  to  the 
other  does  not  occur  at  a  definite  temperature,  and  is  not 
reversible  by  heat  alone. 

Ammonium  nitrate  is  an  example  of  a  substance  belong- 
ing to  the  first  class ;  the  rhombic  crystals  of  this  salt,  which 
separate  at  ordinary  temperatures  from  an  aqueous  solution, 
melt  at  (about)  168°;  as  the  molten  mass  cools  crystals  belong- 
ing to  the  regular  system  are  formed,  but  at  (about)  125° 
these  change  to  rhombohedral  forms,  which  at  (about)  87°  are 
converted  into  rhombic  needles,  from  which,  at  30°  or  so,  the 
original  rhombic  crystals  are  produced.  If  the  rhombic 
crystals  are  again  slowly  heated,  the  rhombic  needle-shaped 
crystals  form  at  (about)  30°;  the  rhombohedral  forms  appear 
at  (about)  87°,  the  regular  crystals  at  (about)  125°,  and  finally 
the  solid  melts  at  198°.  Again,  if  a  little  sulphur  is  melted 
on  a  microscopic  slide  (under  a  cover),  and  the  slide  is 
arranged  so  that  temperature  can  be  easily  regulated1,  mono- 
clinic  crystals  are  produced,  but,  as  temperature  falls,  these 
change  into  rhombic  forms,  and  it  is  possible  to  regulate  the 
temperature  so  that  definite  amounts  of  each  form  exist 
simultaneously,  but  on  the  slightest  change  of  temperature 
the  rhombic  crystals  grow  at  the  expense  of  the  monoclinic, 
or  vice  versa. 

The  behaviour  of  dibromopropionic  acid  when  heated 
illustrates  the  nature  of  the  changes  which  characterise  sub- 
stances belonging  to  Lehmann's  second  class  of  physical 
isomerides.  This  substance  crystallises  in  rhombic  forms 
which  melt  at  64°  (about) ;  if  the  molten  mass  is  heated  a 
few  degrees  above  this  point  rhombic  crystals  (M.P  =  64°) 

1  Lehmann  describes  an  apparatus  for  this  purpose  (loc.  cit.  pp.  102 — 3). 


§  95]  ATOMIC   AND   MOLECULAR   SYSTEMS.  l8/ 

are  again  produced  on  cooling;  but  if  the  molten  substance 
is  heated  many  degrees  above  64°  and  is  then  allowed  to 
cool,  small  flat  nearly  right-angled  tables  are  obtained  which 
melt  at  51°  (about).  If  the  less  stable  form  (M.P.=  $i°)  is 
slowly  heated  under  the  microscope,  growth  of  the  other 
(more  stable)  crystals  is  noticed  ;  the  growth  at  first  is  rapid, 
then  slower,  but  before  the  change  has  gone  far  the  melting 
point  of  the  less  stable  crystals  is  reached  and  the  whole  mass 
becomes  liquid.  If  the  more  stable  form  is  melted,  heated 
some  degrees  above  64°  and  then  brought  into  contact  with 
crystals  of  both  forms,  growth  of  each  modification  proceeds 
until  the  crystals  touch,  after  which  the  more  stable  (higher 
melting)  crystals  grow  into  the  others  until  the  latter  are  com- 
pletely changed  into  the  stabler  forms.  Another  instance  is 
furnished  by  paranitrophenol.  This  compound  crystallises 
from  hot  aqueous  solutions  in  monoclinic  crystals,  and  from 
cold  aqueous  (or  alcoholic)  solutions  in  crystals  belonging  to 
the  same  system  but  differing  in  form  and  melting  point  from 
the  others.  By  fusing  either  form  and  allowing  the  molten 
mass  to  cool,  only  the  less  stable  (lower  melting)  crystals 
are  produced  ;  but  if  a  little  of  the  substance  is  melted 
on  a  microscopic  slide,  and  a  crystal  of  the  second  (stabler) 
form  is  placed  in  contact  with  the  edge  of  the  solidified 
mass,  and  heating  is  then  again  commenced,  crystals  of  the 
stabler  form  begin  to  grow  at  the  expense  of  the  other  crys- 
tals, at  first  rapidly,  then  more  slowly,  until  both  forms 
melt,  the  less  stable  at  a  lower  temperature  than  the  more 
stable. 

95.  I  do  not  think  that  a  rigid  classification  of  physical 
isomerides  into  two  groups  can  be  carried  out.  The  examples 
given  shew  that  there  are  certain  broad  differences  between 
the  two  classes  ;  but  a  detailed  consideration  of  these  ex- 
amples, and  of  others  to  be  found  in  Lehmann's  paper,  seems 
to  me  to  lead  to  the  conclusion  that  there  exists  no  firmly 
drawn  line  of  separation  between  the  phenomena  exhibited 
by  substances  placed  in  different  classes.  This  will,  I  think, 
be  more  apparent  if  some  of  the  facts  enumerated  are  repre- 
sented in  a  roughly  graphic  manner.  Let  us  compare  the 


1 88  CHEMICAL   STATICS.  [§95 

action  of  heat  on  ammonium  nitrate,  dibromopropionic  acid, 
and  paranitrophenol. 

Let  that  form  of  ammonium  nitrate  which  crystallises  in 
regular  crystals  be  called  A,  that  which  crystallises  in  rhom- 
bohedral  forms  B,  that  in  rhombic  needles  C,  and  that  in 
ordinary  rhombic  forms  D.  Let  the  line  ab  represent  the 
b  !68°  interval  of  temperature  through  which  ordinary  am- 
monium nitrate  must  be  heated  until  it  melts ;  now 
125°  let  the  molten  substance  cool,  that  part  of  the  line 
•  g  „  ab  between  168°  and  125°  represents  the  temperature- 
interval  through  which  the  salt  exists  in  form  A, 
--  3<5°  that  part  between  125°  and  87°  represents  the  tem- 
perature-interval through  which  form  B  is  stable, 
that  part  between  87°  and  36°  the  interval  through 
which  form  C  is  stable,  and  lastly  the  portion  below  36°  repre- 
sents the  interval  of  stability  for  form  D.  The  operation 
represented  by  the  line  ab  is  reversible  ;  whether  we  begin 
at  a  or  b,  the  salt  goes  through  the  several  stages  roughly 
indicated  in  the  diagram. 

Now  turn  to  dibromopropicnic  acid.    Let  the  rhombic  form 
melting  at  64°  be  called  A,  and  the  small  tables  melting  at 
51°  be  called  B.      The  line  ab  represents  the  temperature- 
interval  through  which  A  is  stable  ;  on  heat- 
ing  A  to  64°  it  melts,  but  on  cooling,  it  so  to 
speak  runs  back  along  the  same  line:  now  let 
°  A   be  raised  from  a  to  c,  say   1 6°  above  its 


melting  point,  and  then  allowed  to  cool ; 
a  new  substance.  B,  has  been  produced,  and 
this  substance  is  stable  throughout  the  inter- 
val ce  (between  d  and  e  it  is  solid,  between 
c  and  d  it  is  liquid).  Although  B  cannot  be 
changed  into  A  by  heat  alone,  yet  when  B  is  somewhere 
between  c  and  d  (i.e.  when  it  is  molten)  it  may  be  partially 
converted  into  A  by  contact  with  small  portions  of  A.  If 
the  symbols  A  and  B  are  used  to  represent  the  two  forms  of 
paranitrophenol,  then  B  may  be  almost  wholly  converted  into 
A  by  contact  with  A.  Because  of  its  lower  melting  point,  B 
has  been  called  the  less  stable  form  of  dibromopropionic  acid, 


§95]  ATOMIC  AND   MOLECULAR   SYSTEMS.  189 

but  if  we  consider  that  it  cannot  be  changed  into  A  by  the 
action  of  heat  we  should  say  that,  thermally  looked  at,  B  is 
the  more  stable  form  of  this  substance. 

If    we    now    treat    the    facts    concerning    the    diphenyl 
derivative  mentioned  on  p.  184,  par.  92,  dia- 
grammatically  we  shall  have  this  result :  (let 
the  form  melting  at  195°  =  A,  and  that  melt- 
ing at  99°  =  B).     The  line  ab  represents  the 
temperature-interval  through  which  A   must 
be  raised  in  order  to  melt  it :   let  the  molten 
substance  cool  slowly,  it  runs  back  along  the 
same    line   ab\    [?    do   any   crystallographic 
changes  occur  along  this  line] ;  but  let  A  cool 
quickly,  it  seems  to  get,  so  to  speak,  shunted 
off  the  line  of  normal  stability  on  to  the  line 
bd\  cd  represents  the  interval  through  which  it  exists  in  solid 
form  and  ce  the  interval  (roughly)  through  which  it  is  stable 
in  liquid  form,  for  when  B  has  again  been  heated  to  125° — 
130°  it  solidifies,  and  is  found  to  have  come  back  to  form  A, 
i.e.  to  the  line  of  normal  stability1  (ab). 

This  diphenyl  derivative  appears  to  belong  to  both  of  Leh- 
mann's  classes  :  some  of  the  changes  which  it  undergoes  are 
to  a  great  extent  reversible  and  occur  at  definite  temper- 
atures, others  are  not  reversible  and  occur  gradually  through- 
out a  considerable  interval  of  temperature. 

Substances  of  which  ammonium  nitrate  is  the  type  ap- 
pear to  be  less  profoundly  modified  by  the  action  of  heat  than 
substances  belonging  to  the  class  represented  by  dibromopro- 
pionic  acid.  Substances  belonging  to  the  first  of  these  classes 
shew  analogies  with  the  so-called  molecular  compounds  (e.g. 
compare  the  action  of  heat  on  crystallised  sodium  phosphate, 
or  on  hydrated  cobalt  salts2,  with  that  on  dibromopropionic 
acid  or  on  paranitrophenol) ;  and  the  course  of  the  change 
brought  about  by  the  action  of  heat  on  these  bodies  shews 

1  It  seems  probable  that  if  A  were  heated  to  195°  and  cooled  quickly  to  130°, 
and  then  very  rapidly,  it  would  solidify  at  that  point,  and  afterwards  be  found  to 
melt  at  195°. 

2  See  post,  section  5,  par.  102. 


190  CHEMICAL   STATICS.  [§95 

some  analogies  with  the  processes  of  gaseous  dissociation1. 
For  these  reasons  Lehmann  has  summarised  the  phenomena 
characteristic  of  bodies  of  this  class  under  the  term  physical 
polymerism,  and  the  phenomena  characteristic  of  bodies  of  the 
other  class  under  the  term  physical  metamerism.  The  former 
term  implies  that  the  physically  different  forms  exhibited  by 
a  substance  belonging  to  this  class  are  to  be  regarded  as  as- 
sociated with  the  existence  of  physical  molecules,  each  formed 
by  the  grouping  together  of  a  different  number  of  chemical 
molecules  (as  defined  in  Chap.  I.  par.  13,  p.  25).  The  term 
physical  metamerism  on  the  other  hand  implies  that  the 
physical  molecule  of  each  different  form  of  a  substance 
belonging  to  this  class  is  composed  of  the  same  number  of 
chemical  molecules,  but  that  the  arrangement  of  these  is 
different  in  each  case. 

Lehmann's  classification  is  certainly  based  on  no  fanciful 
analogies.  Polymerism  and  metamerism  are  well  marked 
phenomena  among  gaseous  molecules ;  and  the  hypothesis  of 
the  existence  of  groups  of  molecules  characterised  by  definite 
properties,  but  each  of  which  groups  is  readily  decomposed  by 
heat;  appears  to  be  as  simple  as  any  other  that  can  be  pro- 
posed to  explain  the  observed  facts.  Moreover  this  hypo- 
thesis is  almost  forced  on  our  acceptance  when  we  consider 
the  numerous  and  varied  phenomena  summarised  in  the  term 
*  molecular-compounds2.'  But  the  analogy  between  the  reac- 
tions of  gaseous  molecules  and  the  changes  undergone  by 
solid  and  liquid  substances  may  be  pushed  too  far ;  we  ought 
to  recognise  how  small  and  inexact  our  knowledge  is  of  the 
molecular  actions  of  the  latter  classes  of  bodies.  Qualification 
of  the  terms  molecule,  polymerism,  and  metamerism  by  the 
adjective  physical  widens  the  meanings  of  these  terms  by 
making  them  applicable  to  a  larger  class  of  phenomena,  but 
at  the  same  time  it  makes  the  application  less  precise3. 

1  See  Book  II.  Chap.  n. 

2  See  post,  section  5. 

3  Lehmann   considers   in  considerable   detail   the   phenomena   attending   the 
change  of  one  form  of  a  substance  into  another ;    he  divides  the  changes  into 
groups,  according  as  both  forms  are  solid,  or  one  solid  and  one  liquid,  &c.     As  the 


§  96]  ATOMIC   AND   MOLECULAR   SYSTEMS.  IQI 

96.  We  have  thus  found  that  to  trace  the  connections  be- 
tween the  composition  and  the  properties  of  changing  material 
systems  has  always  been  regarded  as  the  fundamental  problem 
of  chemistry.  Attention  has  sometimes  been  almost  confined 
to  the  composition  of  substances  forming  such  systems,  at 
other  times  the  properties  of  the  system  and  its  components 
have  been  regarded  as  chiefly  important.  We  found  that  as 
chemistry  advanced  it  became  necessary  to  know  more  than 
the  mere  elementary  composition  of  bodies ;  having  gained 
the  atom  and  the  molecule,  chemists  were  soon  convinced  that 
the  arrangement  of  the  same  atoms  might  vary,  and  that 

subject  is  important  I  give  a  brief  resume  of  some  of  Lehmann's  results  in  this 
note,  but  the  original  paper  ought  to  be  studied  by  all  who  are  interested  in  the 
subject. 

A.  Change  of  one,  more  complex,  solid  form  of  isomeride  to  another,  less 
complex,  solid  form,  attended  with  absorption  of  heat ;  physical  molecules 
of  both  kinds  are  present  simultaneously,  but  at  a   certain   temperature 
change  will  occur.     If  one  modification  is  heated  alone,  the  normal  tem- 
perature of  change  may  be  largely  exceeded  without  a  complete  change  to 
the  second  modification,  but  at  such  a  high  temperature  contact  with  the 
second  modification  may  determine  sudden  and  complete  change. 

B.  Change  of  solid  form  to  liquid  form,  occurring  with  heat  absorption  at  a 
definite  temperature  dependent  on  the  pressure;    the  change  will  not  be 
complete,  as  molecules  of  both  kinds  will  exist  together.     If  the  specific 
gravity  of  the  solid  form  is  greater  than  that  of  the  liquid  form,  then  on 
heating  past  the  melting  point  there  will  be  rapid  expansion  as  the  physical 
molecules  of  the  solid  form  are  separated  into  those  of  the  liquid  ;  this  will 
be  followed  by  a  slower  regular  expansion.     If  the  specific  gravity  of  the 
solid  is  less  than   that    of  the   liquid,  expansion  will   be   small,  or  even 
negative,  until  a  point  of  maximum  density  is  reached,  after  which  expan- 
sion will  proceed  at  the  normal  rate. 

In  som'e  cases  a  solid  form  is  changed,  by  the  action  of  heat,  into  a 
liquid  form,  which,  at  a  higher  temperature,  is  again  changed  into  a  second 
solid  form,  e.g.  when  selenion  is  heated  till  it  becomes  viscous  and  is  kept 
at  this  temperature  for  some  time  it  changes  into  a  crystalline  form.  So  in 
the  change  of  yellow  to  red  phosphorus  by  the  action  of  heat ;  in  this  case 
the  molecules  which  form  the  liquid  phosphorus  are  kept  apart  for  some 
time,  by  the  energy  added  as  heat  acting  against  cohesion,  and  so  are 
allowed  to  re-arrange  themselves  in  loose  groups. 

C.  Change  of  liquid,  to  solid  modification  is  complex :  a  few  crystals  form 
and  determine  the  crystallisation  of  the  whole  mass  ;   in  some  cases  the 
liquid,  especially  if  viscous,  may  be  cooled  below  the  temperature  at  which 
crystallisation  normally  begins,  and  may  then  pass  into  an  amorphous  solid 
form. 


CHEMICAL   STATICS.  [§  96 

properties  might  therefore  be  correlated  not  only  with  atomic 
composition  but  also  with  atomic  configuration.  We  traced 
this  conception  through  the  dualism  of  Berzelius  and  the 
unitary  system  of  Dumas,  Laurent,  Gerhardt  and  others, 
through  the  hypothesis  of  compound  radicles  and  that  of 
types,  to  the  time  when  Frankland  and  Kekule  gave  it 
greater  precision  by  arranging  the  elementary  atoms  in 
groups  according  to  the  maximum  number  of  other  atoms 
with  which  each  was  found  to  combine. 

But  we  saw  that  the  expression  equivalency  (or  valency) 
of  atoms  gradually  came  to  be  used  in  a  loose  and  inexact 
manner.  We  found  that  the  comparison  of  monovalent  with 
divalent,  &c.  atoms,  when  unchecked  by  accurate  dynamical 
knowledge,  led  to  the  belief  that  the  term  in  question  expressed 
in  some  vague  way  quantitative  measurements  of  interatomic 
forces,  and  to  the  conclusion  that,  inasmuch  as  one  divalent 
atom  could  directly  bind  to  itself  two  other  atoms,  while  one 
monovalent  atom  could  act  directly  on  only  a  single  other 
atom  in  a  molecule,  therefore  the  divalent  atom  was  capable 
of  exerting  twice  as  much  force  as  the  monovalent  atom. 
The  latter  part  of  the  foregoing  sentence  may  I  think  be 
taken  as  fairly  representative  of  the  loose  and  slipshod  way 
in  which  dynamical  language  has  too  often  been  used  in 
chemistry. 

We  found  that  attempts  were  made  to  build  a  general 
theory  of  valency  on  a  shifting  quasi-dynamical  foundation ; 
but  the  account  given  in  this  section  of  Lossen's  criticisms  of 
the  expressions  '  a  bond,'  '  a  valency,'  '  a  unit  of  affinity/  &c. 
has  I  think  been  sufficient  to  shew  how  inexact,  while  appar- 
ently precise,  and  how  narrow,  while  apparently  far-reaching, 
the  theory  in  question  really  is. 

The  objections  raised  against  the  atomic  theory  in  recent 
years  by  some  chemists,  who  nevertheless  made  free  use  of 
the  essentially  atomic  conceptions  of  modern  chemistry,  led, 
it  seems  to  me,  to  a  looseness  of  thinking  about  atoms,  mole- 
cules and  equivalents,  which  has  done  no  little  harm.  Parts 
by  weight  were  spoken  of  as  if  the  expression  were  synony- 
mous with  atom;  equivalents  were  regarded  as  acting  and 


§  96]  ATOMIC   AND   MOLECULAR   SYSTEMS.  1 93 

reacting  one  on  the  other ;  there  appeared  to  be  a  possibility 
of  chemistry  retracing  her  steps  to  the  time  when  no  precise 
meaning  was  attached  to  any  of  the  terms  atom,  molecule, 
combining  weight,  equivalent,  but  each  was  used  as  nearly 
synonymous  with  the  others.  From  the  possibility  of  such 
retrogression  we  have  been  saved  by  the  general  advance  of 
physical  science.  As  the  molecular  theory  of  matter  became 
more  precise  and  its  applications  more  far-reaching,  it  was 
impossible  for  chemists  to  employ  conceptions  essentially 
molecular  and  atomic  and  at  the  same  time  to  express 
chemical  changes  in  a  notation  based  on  the  notions  of  a 
pre-molecular  era.  It  became  necessary  to  choose  definitely 
between  the  atom  and  the  equivalent,  and  the  great  body  of 
chemists  has  certainly  chosen  the  former. 

But  as  soon  as  attempts  to  found  a  theory  of  chemical 
actions  on  the  basis  of  equivalents  was  abandoned,  it  was 
seen  that  the  conception  of  equivalency  might  be  retained 
and  applied  to  the  elementary  atoms.  To  keep  distinct  the 
conceptions  implied  in  the  terms  equivalent  and  atom,  and  at 
the  same  time  to  arrange  the  atoms  in  equivalent  groups,  is 
one  of  the  problems  of  modern  chemistry.  On  this  distinction 
and  on  this  resemblance  is  based  the  theory  of  isomerism. 
The  study  of  isomerism  has  done  much,  we  found,  to  render 
precise  the  conception  of  the  molecule  as  a  structure  with 
properties  dependent  on  the  nature,  the  number,  and  the 
arrangement  of  the  constituent  atoms. 

We  endeavoured  to  subdivide  the  conception  expressed  in 
the  words  'arrangement  of  atoms  in  a  molecule'  into  parts, 
and  to  demonstrate  by  illustrations  the  existence  of  a  connec- 
tion between  each  of  these  parts  and  the  properties  of  the 
molecule.  These  illustrations  led  to  clearer  notions  concern- 
ing valency  of  atoms,  and  the  meaning  of  structural  formulae ; 
these  formulae  we  regarded  as  expressing  the  actual  valencies 
of  the  atoms  in  the  molecule, — i.e.  the  number  of  atoms 
directly  acting  on  and  acted  on  by  each  atom, — and  as  ex- 
pressing also  the  distribution  of  the  atomic  interactions,  i.e. 
the  nature  of  the  atoms  in  direct  mutual  connection ;  but  we 
tried  to  attach  no  quantitative  meaning  to  the  symbols  used 

M.  C.  13 


194  CHEMICAL  STATICS.  [§  97 

for  expressing  atomic  valencies  and  distributions  of  atomic 
interactions. 

The  theory  of  valency,  as  thus  used,  leads  to  dynamical 
conceptions,  but  regards  these  as  outside  its  sphere:  it  points 
the  way  along  which  progress  will  be  made.  Attempts  must 
be  made  to  apply  thermal,  optical,  and  other  physical  methods 
of  research  to  the  investigation  of  chemical  problems;  thus 
we  may  hope  to  gain  clear  and  precise  knowledge  regarding 
the  connection  between  structure  and  stability  of  molecules, 
in  so  far  as  the  latter  is  measured  by  variations  in  the 
quantities  of  energy  associated  with  each  molecule. 


APPENDIX  TO  SECTION  IV. 

97.  To  have  given  a  detailed  account  of  Lossen's  criticisms 
of  the  generally  accepted  views  regarding  'valencies'  or  'units 
'of  affinity'  in  the  text  of  the  section  on  isomerism,  would 
have  involved  too  great  an  interruption  of  the  main  argument 
of  that  section.  But  as  Lossen's  criticisms  seem  to  me  of 
great  importance  I  propose  to  give  some  account  of  them 
here. 

The  many  and  varied  hypotheses  concerning  valency  set 
forth  by  chemists  of  acknowledged  authority  may  be  divided, 
says  Lossen,  into  three  groups : — 

I.  Those  hypotheses  which  regard  'an  affinity'  as  a  defi- 
nite quantity  of  matter,  or  as  an  action  of  some  kind  pro- 
ceeding from  a  definite  quantity  of  matter. 

II.  Those  which  regard  'an  affinity'  as  a  part  of  an  atom, 
or  at  least  as  something  connected  with  a  part  of  an  atom. 

III.  Those  which  regard  the  'affinities'  of  an  atom  as 
definite  forms  of  motion  of  the  atom. 

I.  Erlenmeyer1  has  developed  the  conception  of  'Ajffini- 
'  valencies?  He  states,  as  a  rule  without  exceptions,  that  'in  all 
'chemical  combinations  a  constant  quantity  of  one  element 

1  For  references  to  the  work  of  the  various  chemists  mentioned,  see  Lossen, 
loc.  dt. 


§  97]  ATOMIC  AND   MOLECULAR  SYSTEMS.  IQ5 

'always  attracts  a  constant  quantity  of  another.'  These 
constant  quantities  are  the  'affinivalencies'  of  the  elements : 
one  affinivalency  of  element  a  always  binds  to  itself  one 
affinivalency  of  element  b.  The  affinivalency  of  carbon  =  3,  of 
oxygen  =  8.  In  CO2  we  have  3  parts  by  weight  of  carbon 
combined  with  8  of  oxygen,  but  in  CO  the  same  amount  of 
carbon  with  only  4  parts  by  weight  of  oxygen ;  Erlenmeyer's 
general  law  is  therefore  erroneous.  If  it  be  said  that  a 
constant  quantity  of  one  element  attracts  (not  combines  with) 
a  constant  quantity  of  another,  then,  as  in  CO2  6  parts  by 
weight  of  carbon  attract  16  of  oxygen,  we  must  suppose  that 
in  CO  1 6  parts  by  weight  of  oxygen  are  attracted  by  6  of 
carbon,  and  that  the  remaining  6  of  carbon  have  no  attractive 
action  on  the  oxygen. 

Atoms  and  relative  quantities  of  matter  are  compared  by 
Erlenmeyer,  but  relative  quantities  do  not  attract  each  other. 
In  the  molecule  CO  there  is  one  atom  of  carbon  and  one 
atom  of  oxygen,  and  these  atoms  attract  one  another;  half  an 
atom  cannot  attract  because  it  has  no  existence.  The  hypo- 
thesis that  an  atom  is  nonhomogeneous,  although  indivisible, 
might  be  made,  but  is  not  made,  by  Erlenmeyer.  If  an  equiva- 
lent is  regarded  as  a  constant  quantity,  this  quantity  attracts 
sometimes  one,  sometimes  two  (or  more)  equivalents  of  other 
elements.  The  molecule  CH4  contains  one  atom  of  carbon  and 
four  atoms  of  hydrogen ;  we  may  say  that  3  parts  by  weight 
of  carbon  here  attract  I  part  by  weight  of  hydrogen:  so  in 
CC14  it  may  be  said  that  3  parts  of  carbon  attract  35*5  parts  of 
chlorine.  But  in  CH3C1  12  parts  of  carbon  attract  3  parts  of 
hydrogen  and  35*5  parts  of  chlorine;  in  place  of  12  parts  of 
carbon  we  may,  if  we  choose,  say  9+3  parts,  just  as  we  might 
say  that  7+5  =  12,  or  ^144=12;  but  we  cannot  say  that 
9  parts  of  carbon  attract  3  parts  of  hydrogen  and  the  re- 
maining 3  parts  of  carbon  attract  the  35*5  parts  of  chlorine. 
If  we  suppose  the  carbon  atom  to  be  perfectly  homogeneous, 
then  the  whole  atom  acts  on  the  chlorine  atoms  and  on  each 
of  the  hydrogen  atoms:  if  we  suppose  that  the  atom  of 
carbon  is  possessed  of  a  structure,  it  remains  to  explain  in 
what  respect  one  part  of  the  atom  differs  from  other  parts; 

13—2 


196  CHEMICAL  STATICS.  [§  97 

but  a  part  of  an  atom  is  not  the  same  thing  as  a  fraction  of  the 
relative  weight  of  an  atom. 

Hofmann  speaks  of  'an  affinity'  as  a  force  proceeding  from 
a  constant  mass  of  an  element,  which  mass  he  regards  as  the 
equivalent,  and  defines  it  as  'the  minimum  atom-binding 
quantity'  of  the  element.  He  nevertheless  uses  equivalent  as 
a  varying  quantity.  By  an  arbitrary  choice  of  certain  values 
for  the  equivalents  of  the  elements  it  is  possible  that  the 
number  obtained  by  dividing  the  atomic  weight  by  the 
equivalent  weight  of  any  element  should  be  the  same  as  the 
number  expressing  the  maximum  number  of  hydrogen  atoms 
which  can  be  bound  by  one  atom  of  the  given  element. 

L.  Meyer  also  speaks  of  the  action  of  quantities  by  weight 
of  one  element  on  atoms  of  another  element.  In  one  place  he 
defines  equivalent  quantities  of  elements  as  those  quantities 
which  are  able  to  bind  to  themselves,  directly  and  without  the 
intervention  of  a  third  substance,  equal  quantities  of  other  sub- 
stances. We  should  expect  16  parts  by  weight  of  oxygen  to  be 
equivalent  to  12  parts  by  weight  of  carbon,  and  to  14  parts  by 
weight  of  nitrogen,  because  16  parts  of  oxygen  directly  bind 
1 6  of  oxygen  in  O2,  14  of  nitrogen  in  NO,  and  12  of  carbon 
in  CO :  but  L.  Meyer  supposes  two  free  affinities  in  the  last 
named  molecule,  i.e.  he  supposes  that  ^  carbon  bind  16  of 
oxygen,  although  the  molecule  CO  contains  one  indivisible 
atom  of  carbon  and  one  indivisible  atom  of  oxygen. 

Those  hypotheses  in  which  ' affinities'  are  regarded  as 
constant  weights  of  matter,  or  as  actions  proceeding  from 
constant  weights,  arise,  according  to  Lessen,  from  not  suffi- 
ciently marking  the  distinction  between  equivalent  and  atom. 
Equivalent,  or  combining,  weights  are  relative  weights  of 
divisible  masses;  atomic  weights  are  relative  weights  of 
indivisible  masses.  If  the  atomic  hypothesis  is  adopted,  we 
must  regard  atomic  weights  as  relative  weights  of  mutually 
reacting  bodies;  but  equivalent  weights,  in  so  far  as  they 
differ  from  atomic  weights,  are  relative  weights  of  imagined 
sums,  or  fractions,  of  these  bodies.  Bodies,  whose  relative 
weights  are  equal  to  these  equivalent  weights,  do  not  mutually 
react  within  molecules.  To  find  equivalents,  parts  by  weight 


§  97]  ATOMIC  AND   MOLECULAR   SYSTEMS.  1 97 

should   be  compared   with   parts   by  weight,  or  atoms  with 
atoms. 

II.  Besides  the  hypothesis  of  'affinivalencies'  already 
referred  to,  Erlenmeyer  also  speaks  of  mutual  actions  between 
atoms  as  occurring  at  certain  points  of  these  atoms.  This 
may  mean  either  that  contact  (not  of  course  absolute  contact) 
between  the  reacting  atoms  is  made  at  these  points,  or  that 
mutual  atomic  action  occurs  only  when  these  attracting  points 
coincide.  The  attracting  points  must  be  considered  as 
qualitatively  different  from  the  rest  of  the  atoms.  The  form 
of  polyvalent  atoms  must  be  such  that  several  points  of  one 
can  touch  the  same  number  of  points  of  another :  the  positions 
of  the  points  must  be  such  that  when  some  of  these  points 
are  in  contact  it  is  not  necessary  that  all  should  be  in  contact. 
To  fulfil  these  conditions  without  supposing  the  form  of  the 
atoms,  or  at  any  rate  the  positions  of  "the  points,  changeable, 
is  exceedingly  difficult.  This  hypothesis  of  Erlenmeyer  tends 
to  foster  the  notion  of  an  attractive  force  proceeding  from 
different  points  of  elementary  atoms;  Kekule's  graphic  for- 
mulae do  not,  probably,  imply  this  conception,  but  these 
formulae  may  be,  and  have  been,  used  as  if  this  conception 
were  true. 

A  qualitative  difference  between  parts  of  an  atom,  can 
only  mean  that  some  parts  are  chemically  active  while  others 
are  chemically  inactive.  If  the  inactive  parts  are  composed  of 
imponderable  matter  then  each  w-valent  atom  must  be  made 
up  of  n  atoms ;  we  thus  arrive  at  atomic  weights  different 
from  those  on  which  the  science  of  chemistry  at  present  rests. 
If  the  inactive  parts  consist  of  ponderable  matter,  then  in  the 
case  of  action  between  different  atoms  we  have  action  through* 
the  ether,  but  in  the  case  of  action  between  parts  of  the  same 
atom  we  have  action  through  ponderable  chemically  inactive 
matter.  In  either  case  it  appears  that  the  notion  of  atom 
must  be  very  different  from  that  at  present  adopted,  and,  it 
would  seem,  necessarily  adopted,  if  facts  are  to  be  explained. 

But  it  may  be  supposed  that  the  active  parts  of  the  atom 
are  in  a  different  electrical  condition  from  the  inactive  parts. 
If  electricity  be  a  form  of  motion,  then  some  parts  of  an  indi- 


198  CHEMICAL   STATICS.  [§  97 

visible  atom  must  be  supposed  in  motion  while  others  are 
not ;  if  electricity  be  a  fluid,  then  we  have  a  material  differ- 
ence, arising  from  the  partial  fixation  of  this  fluid,  between 
the  active  and  inactive  parts  of  the  atom.  Both  of  these 
hypotheses  are  opposed  to  the  fundamental  conception  of 
atom1. 

Michaelis  has  supposed  that  the  attractive  force  of  an 
atom  is  exerted  in  certain  fixed  directions  only.  On  this 
hypothesis  a  straight  line  joining  two  atoms  which  are 
directly  bound  together  may  be  regarded  as  expressing  the 
direction  of  the  mutually  exerted  force  ;  an  ^-valent  atom  has 
n  such  directions.  If  this  atom  is  directly  bound  to  fewer 
than  11  atoms,  say  to  n—  x  atoms,  then  the  mutual  action  is 
exerted  in  n—  x  directions.  Lessen  expresses  his  general  agree- 
ment with  this  interpretation  of  the  hypothesis  of  Michaelis. 
But  if  that  chemist  supposes  that  to  every  atom,  regarded  as 
a  point,  there  are  always  attached  a  fixed  number  of  such 
*  lines  of  force/  then  it  is  asked  '  on  what  does  the  atom  act 
when  it  is  bound  to  less  than  its  maximum  number  of  other 
atoms  ? ' 

The  objection  urged  to  van't  Hoff's  form  of  the  hypothe- 
sis now  being  discussed,  is,  that  by  this  chemist  the  '  affinities  ' 
of  an  atom  are  imagined  as  arranged  in  a  definite  form  in 
space ;  but  as  we  cannot  define  an  '  affinity,'  much  less  can 
we  assign  geometrical  figures  to  the  arrangement  of  these 
'  affinities.' 

III.  L.  Meyer  supposes  that  there  is  one  position  at 
which  a  monovalent  atom  during  its  vibration  can  combine 
with  another  atom  to  form  a  stable  compound,  that  there  are 
'two  positions  at  which  a  divalent  can  combine  with  another 
atom,  and  so  on.  In  the  molecule  NH3  we  have  one  triva- 
lent  and  three  monovalent  atoms  ;  the  nitrogen  atom  swings 
through  three  positions,  at  each  of  which  it  can  take  up  one 
hydrogen  atom.  In  the  molecule  OH2  the  divalent  oxygen 

1  This  criticism  is  rather  weak :  we  know  too  little  as  to  what  electricity  is  to 
hazard  such  criticism  as  this ;  besides,  Helmholtz  has  shewn  that  there  is  probably 
a  close  and  definite  connection  between  the  valency  of  an  atom  and  the  electrical 
charges  on  that  atom;  see  book  n. 


§§  97>  98]        ATOMIC  AND   MOLECULAR   SYSTEMS.  199 

atom  swings  through  two  such  positions.  In  the  molecule 
NO  it  appears  as  if  the  three  positions  of  possible  combina- 
tion passed  through  by  the  triad  nitrogen  atom  must  be  also 
touched  by  the  path  of  the  diad  oxygen  atom,  but  if  so  the 
oxygen  atom  may,  in  some  circumstances,  be  trivalent. 

The  results  of  O.  E.  Meyer's  physical  and  dynamical  in- 
vestigation of  the  forms  of  molecules  are  not  in  harmony  with 
this  view  of  L.  Meyer.  The  form  of  a  molecule  would  appear 
to  be  dependent  more  on  the  number  of  the  constituent  atoms 
than  on  the  valencies  of  these  atoms.  But  on  L.  Meyer's 
hypothesis  the  nature  of  the  path  of  the  atoms  swinging  in 
the  molecule  must  condition  the  form  of  the  molecule,  and 
the  nature  of  this  path  is  itself  conditioned  by  the  valencies  of 
the  atoms. 

Kekule  has  advanced  hypotheses  as  to  the  motion  of 
atoms  within  molecules,  but  these  hypotheses  are  not  suffici- 
ently definite  to  admit  of  detailed  criticism.  Lessen  however 
objects  to  applying  to  the  motion  of  atoms  within  molecules 
the  conceptions  which  arise  from  a  study  of  the  motion  of 
molecules  in  a  confining  vessel.  If  the  atoms  composing  a 
mass  of  hydrogen  molecules  undergo  mutual  collisions,  why, 
when  they  have  separated  a  certain  distance  from  one 
another,  is  the  direction  of  their  motion  changed  until  a 
second  collision  occurs  ?  There  is  no  confining  molecular 
wall  answering  to  the  sides  of  a  containing  vessel.  If  it  be 
supposed  that  the  atoms  in  molecule  a  enter  into  collision 
with  the  atoms  in  molecule  b  or  c,  then  this  is  equivalent 
to  asserting  that  a  mass  of  hydrogen  is  composed  not  of 
diatomic,  but  of  monatomic  molecules1. 

98.  Among  the  various  developments  of  the  bond-theory 
of  valency  not  mentioned  in  the  text,  is  that  which  concerns 
itself  with  the  question  whether  all  the  bonds  of  a  polyvalent 
atom  are  of  equal  value,  or  whether  one  may  be  '  stronger ' 
than  another.  If  the  criticism  applied  to  the  subject  of 

1  Here  again,  I  think  Lessen  carries  his  criticism  too  far.  The  methods  of 
molecular  enquiry  are  necessarily  statistical ;  a  mass  of  hydrogen  may  contain 
many  free  atoms  (or  monatomic  molecules),  and  yet  for  all  practical  purposes 
behave  as  if  composed  entirely  of  diatomic  molecules. 


200  CHEMICAL  STATICS.  [§98 

bonds  generally  is  just,  it  follows,  I  think,  that  the  question 
alluded  to  is  meaningless ;  but  as  it  has  been  hotly  disputed 
about,  it  may  be  well  briefly  to  consider  it  here. 

It  is  assumed  in  the  bond-hypothesis  that  the  so-called 
affinities  of  atoms  attract  or  satisfy  one  another,  and  hence 
those  affinities  of  one  atom  which  are  not  satisfied  by  affini- 
ties of  another,  must  be  satisfied  by  other  affinities  of  the 
atom  itself.  No  molecule,  it  is  sometimes  said,  can  contain 
an  odd  number  of  atoms  of  uneven  valency.  This  outcome1 
of  Gerhardt's  Maw  of  even  numbers'  (see  ante,  chap.  I, 
par.  36)  is  however  contradicted  by  the  existence  of  the 
molecules  I,  NO,  NO2,  C1O2,  WC15,  VC14  or  VOC13,  and 
cannot  therefore.be  accepted  as  a  statement  of  facts,  unless 
indeed  the  valency  of  an  atom  is  a  number  susceptible  of 
arbitrary  variation.  That  the  maximum  valency  of  each 
atom  is  fixed  is  generally  admitted.  One  school  however 
holds  that  (e.g.)  a  tetrad  atom  is  always  tetrad,  another  school 
that  a  tetrad  may  function  as  a  diad  atom ;  in  the  molecule  CO, 
for  instance,  the  carbon  atom,  it  is  said,  is  tetrad,  but  two  of  its 
affinities  are  mutually  satisfied.  The  opponents  of  this  view 
would  say  that  in  CO  the  carbon  atom  is  divalent,  the  other 
pair  of  bonds  being  latent.  The  dispute  has  been  wholly 
a  battle  about  words.  Whether  the  bonds  are  latent,  or 
'are  mutually  satisfied,  they  are  equally  existent :  as  Lessen 
remarks,  '  zwei  and  zwei  geb en  dock  immer  vier? 

But  if  always  existent,  are  the  bonds  always  of  equal 
value?  Are  the  two  pairs  of  bonds  which  hold  the  two 
oxygen  atoms  to  the  carbon  in  CO2  equal  in  value  to  twice 
the  pair  of  bonds  by  which  one  oxygen  atom  is  held  to 
a  carbon  atom  in  the  molecule  CO  ? 

Now  if  we  wish  to  compare  things  we  must  have  a 
standard  ;  but  I  think  sufficient  facts  have  been  enumerated 
to  shew  that  no  standard  exists  in  terms  of  which  the  expres- 
sion '  value  of  a  bond  '  may  be  stated.  Even  if  the  valency  of 
an  atom  is  regarded  as  expressing  the  total  number  of  parts 
into  which  the  chemical  energy  of  that  atom  is  divisible,  this 

1  The  statement  is  sometimes  put  in  this  form;  "the  sum  of  the  valencies,  or 
affinities,  of  the  atoms  in  any  molecule  is  always  an  even  number." 


§  98]  ATOMIC  AND   MOLECULAR   SYSTEMS.  2OI 

must  mean,  that  the  energy  is  divisible  when  there  is  mutual 
action  between  the  given  atom  and  other  atoms  in  a  mole- 
cule. Thus,  assume  for  a  moment  that  the  chemical  energy 
of  an  atom  of  carbon  is  divisible  into  four  parts,  it  does  not 
follow  that  each  part  represents  a  fourth  of  the  whole  energy 
or  always  represents  the  same  portion  of  that  energy.  To 
take  an  illustration,  in  the  stable  molecule  CO  we  must  sup- 
pose, on  this  hypothesis,  that  the  whole  of  the  chemical  energy 
of  the  carbon  atom  is  employed  in  the  transaction  symbolised 
by  the  formula  C  —  O  ;  again,  in  O  —  C  —  S  the  whole  of  the 
energy  of  the  carbon  atom  is  employed,  but  the  energy  repre- 
sented by  O  —  C  is  probably  different  from  that  represented 
by  C  —  S,  and  the  sum  of  these  is  probably  different  from  that 
represented  by  the  expression  O  —  C  —  O.  '  The  number  of 
possible  ways  in  which  the  energy  is  distributed  is,  on  this 
hypothesis,  measured  by  the  valency  of  the  atom,  the  amount 
of  the  energy  employed  in  any  atomic  transaction  depends 
on  the  nature  of  the  atom  or  atoms  between  which  and  the 
given  atom  there  is  mutual  intramolecular  action1. 

Even  if  we  adopt  this,  the  most  dynamical  view  of  valency 
that  can  be  adopted  with  any  safety,  the  controversy  con- 
cerning equal  and  unequal  bonds  is  seen  to  be  a  mere 
logomachy2. 

1  For  a  fuller  working  out  of  this  way  of  regarding  valency  see  Claus,  Ber. 
14.  432. 

2  It  is  sometimes  said  that  the  hydrogen  atoms  in  the  molecule  of  benzene  are 
of  equal  value,  but  when  one  of  these  atoms  is  replaced  by  a  radicle,  the  remaining 
five  are  of  different  values  relatively  to  the  radicle  introduced  into  the  molecule. 
To  make  such  a  statement  as  this,  it  seems  to  me,  is  to  employ  the  term  value  in 
too  loose  and  vague  a  way.     All  the  hydrogen  atoms  in  a  molecule  of  a  mono- 
derivative  of  benzene  are  monovalent,  and   therefore  of  equal  value  so  far  as 
'  proportion  in  exchange '  for  chlorine,  bromine  &c.  goes.     What  appears  to  be 
meant   by  the   statement  in   question   is,    that  more   than   one   mono-derivative 
(chloro-  bromo- or  generally  X-  derivative)  can  be  obtained  from  the  mole- 
cule CSH5X;  but  this  is  simply  a  special  illustration  of  the  general  proposition 
that  the  properties  of  compounds  are  not  wholly  dependent  on  the  valencies  of 
their  constituent  atoms. 


202  CHEMICAL   STATICS.  [§§  99,  IOO 


SECTION   V.     Molecular  Compounds. 

99.  The  adjectives  molecular  and  atomic  have  been  em- 
ployed   by    Kekule1    and    others  to  distinguish   those    com- 
pounds which  separate  into  two  or   more   other   substances 
when  heated,  from  those  which  can  be  vaporised  without  de- 
composition.    Ammonium  chloride,  which  when  heated  yields 
a  vapour  containing  ammonia  and  hydrochloric  acid,  may  be 
taken  as  a  typical  molecular  compound,  and  water,  the  vapour 
of  which  contains  only  molecules  of  water-gas,  as  a  typical 
atomic  compound. 

This  division  of  compounds  has  played  an  important  part 
in  the  development  of  the  theory  of  valency.  Kekule  has 
always  insisted  that  facts  regarding  atomic  compounds 
can  alone  be  employed  as  data  for  finding  the  valencies  of 
elementary  atoms ;  his  opponents  have  retorted  by  de- 
manding a  definition  of  molecular  as  opposed  to  atomic 
compounds,  and  by  shewing  that  every  proposed  definition 
fails  when  applied  to  actual  phenomena. 

But  it  is  not  so  much  as  concerns  the  theory  of  valency 
that  the  distinction  implied  in  the  words  atomic  and  mole- 
cular compounds  ought,  I  think,  to  be  insisted  on  ;  if  the 
arguments  put  forward  in  the  preceding  section  are  of  any 
value,  we  must  agree  to  confine  the  theory  of  valency,  at 
present,  to  gaseous  compounds.  There  are  however  many 
and  varied  phenomena,  all  more  or  less  belonging  to  the 
borderlands  between  chemistry  and  physics,  which  may  be 
conveniently  considered  under  the  heading  of  molecular  com- 
pounds. 

100.  And    I  would    begin    by  admitting   that   no  strict 
definition  of  molecular,  as  opposed  to  atomic,  compounds  can 
be  given,  which  shall  enable  us  to  assign  every  disputed  case 
to  its  proper  class.     A  substance  may  yield  a  vapour  which 
is  chemically  homogeneous  below  a  certain  temperature  but 
heterogeneous  above  this  temperature  :  we  cannot  fix  a  limit 

1  See  his  Lehrbuck,  Vol.  I.  pp.  142,  145,  443,  &c. :  also  Compt.  rend.  58.  510. 


§  101]  ATOMIC   AND   MOLECULAR   SYSTEMS.  2O3 

for  each  group  of  compounds  and  say,  that  those  which  yield 
vapours  homogeneous  below  this  temperature  are  atomic, 
while  those  in  the  vapour  of  which  dissociation  begins  below 
the  temperature-limit  are  molecular. 

I  would  again  urge  the  importance  of  remembering  that 
when  we  say  that  a  gas  consists  of  molecules  of  this  or  that 
composition,  we  refer  and  can  refer  only  to  the  average  com- 
position of  the  gas ;  many  molecules  may  be  dissociated  into 
two  or  more  chemically  different  kinds  of  matter,  other 
molecules  may  be  aggregated  into  complex  groups.  Even  in 
an  elementary  gas  at  moderate  temperatures  some  atoms  and 
many  groups  of  molecules  are  probably  present  at  any 
moment:  the  values  obtained  for  the  specific  gravities  of  gaseous 
bromine  and  iodine,  and  for  gaseous  nitrogen  dioxide,  stan- 
nous  chloride,  and  acetic  acid  well  illustrate  the  gradual 
nature  of  the  passage  from  one  average  molecular  state  to 
another1. 

101.  Some  chemists  would  recognise  in  mixtures  of  two 
or  more  liquids,  in  solutions  of  salts,  and  of  gases  (e.g.  CO2) 
in  water,  the  existence  of  molecular  compounds.  In  such 
cases  the  proportions  in  which  the  substances  are  supposed  to 
be  combined  are  very  variable.  It  cannot  be  correct  to  speak 
of  a  molecule  of  the  mixture  of  alcohol  and  water,  or  of  the 
solution  of  salt  in  water,  although  it  may  be  permissible  to 
regard  these  liquids  as  containing  groups  of  molecules  of 
alcohol  and  water,  or  of  salt  and  water. 

There  are  other  actions  wherein  small  changes  in  physical 
conditions  suffice  to  cause  changes  in  the  relative  quantities  of 
substances  combined  in  definite  proportions :  for  instance, 
when  the  substance  containing  water  and  sodium  phosphate 
in  the  proportions  Na2HPO4. 12H2O  is  heated,  it  very  readily 
loses  water  and  becomes  NagHPO^  .  7H2O.  If  by  molecular 
compound  is  meant,  a  loose  combination  in  definite  pro- 
portions of  two  or  more  chemically  different  kinds  of  matter 
so  as  to  produce  another  kind  of  matter  characterised  by 
fairly  definite  properties,  but  readily  undergoing  change,  then 

1  See  par.  roi,  pp.  205,  208 — 9. 


204  CHEMICAL   STATICS.  [§  IOI 

we  may  certainly  say  that  Na2HPO4.  I2H2O  is  a  molecular 
compound. 

Once  more,  compounds  exist  which  are  characterised  by 
very  definite  properties,  but  which,  when  heated,  undergo 
gradual  change  into  two  or  more  substances,  the  original 
compound  being  gradually  re-formed  as  the  vapours  cool. 
Thus  the  formula  PC15  expresses  the  elementary  composi- 
tion of  an  undoubted  chemical  compound  ;  when  this  solid 
substance  is  heated  it  vaporises,  but  the  vapour  can  be 
proved  by  experiment  to  contain  molecules  of  PC13  and  C12, 
along  with  undecomposed  PC15.  The  following  numbers 
shew  the  gradual  progress  of  the  change  which  occurs : 

Calculated  sp.  gr.  of  gaseous  PC15=7'2  1  r  •  _  T 

„  „  gas  consisting  of  PC13+  C12=3'6J  LC 

Number  of  molecules 

Temperature.  Sp.  gr.  of  vapour.  decomposed  per  100 

molecules  of  PCl^.1 

182°  5'08  417 

190  4'99  44'3 

200  4-85  48'5 

230  4-30  67-4 

250  4-00  80-0 

274  3-84  87-5 

288  3-67  96-2 

3oo  3-65  97-3 

The  following  numbers  representing  the  specific  gravities 
of  nitrogen  tetroxide  at  various  temperatures  exhibit  the 
gradual  dissociation  of  molecules  of  N2O4  into  molecules  of 


1  Calculated  by  means  of  the  formula  /=  — ^r where  p=-  number  of 

molecules  decomposed,  D= observed  density  of  gas,  d—  theoretical  density  of 
vapour  supposing  no  dissociation  to  occur.  This  formula  assumes  that  each 
molecule  dissociates  into  two  parts :  if  each  molecule  separates  into  a  parts, 

the  formula  is /=       -    - .        .     See  Naumann,  Lehr-  und  Handbuch  der  Thermo- 

chemie,  pp.  114,  115. 

2  Naumann,  loc.  dt.  p.  117. 


Percentage  molecular 
decomposition. 

Increase  in  percentage 
decomposition  for  each 
rise  of  10°. 

19-96 

— 

25-68 

6-5 

29-23 

8-1 

40*04 

II'O 

52-84 

i2-r 

65-57 

i3'o 

76-6I 

io'4 

84-83 

8-8 

98-69 

r8 

§  101]  ATOMIC  AND   MOLECULAR   SYSTEMS.  2O5 

Temperature.  Sp.  gr.  of  vapour. 

267°  2-65 

35'4  2-53 

39-8  2-46 

49'6  2-27 

60 '2  2 '08 

70 'o  1-92 

80-6  1-86 

96-0  172 

135-0  i -60 

As  N2O4  is  dark-red  and  nearly  opaque,  and  NO2  is  trans- 
parent and  nearly  colourless,  the  change  from  one  compound 
to  the  other  can  be  traced  by  observing  the  colour  of  the 
heated  gas. 

A  study  of  the  specific  gravity  of  the  vapour  obtained  by 
heating  acetic  acid,  at  different  temperatures  and  pressures, 
leads  to  interesting  results,  some  of  which  are  presented  in 
the  following  table. 

Pressure  Sp.  gr.  of  vapour 

Temperature.  (in  millimetres  of  (calculated  sp.  gr.  of 

mercury)  C2H4O2  vapour  =  2'o8). 

120°  760  3'20 

125  760  3'20 

130  760  3'12 

130  60  2'12 

130  30  2-10 

1 60  760  2 '48 

I7O  760  2 '42 

220  760  2*I5 

300  760  2'08 

The  vapour  of  acetic  acid  is  denser  a  few  degrees  above 
the  boiling  point  (B.P.  =  119°)  than  at  a  temperature  100° 
higher ;  the  specific  gravity  decreases  as  the  temperature  rises 
(even  if  the  pressure  is  increased)  until  it  attains  a  constant 
value,  equal  to  the  theoretical  value,  at  about  220°. 

If  the  density  of  acetic  acid  vapour  were  determined  only 
at  120°  and  under  a  pressure  of  760  mm.  we  should  deduce 
the  formula  C3HGO3  as  the  molecular  formula  of  this  com- 
pound. If  the  density  were  determined  at  any  temperature 


2O6  CHEMICAL   STATICS.  [§  IOI 

between  215°  and  300°  (7600101.)  we  should  deduce  the 
molecular  formula  C2H4O2.  Inasmuch  as  the  density  gradually 
decreases  as  the  temperature  rises  from  120°  to  215°,  but 
remains  constant  thereafter,  and  inasmuch  as  experiment  can 
detect  no  chemical  heterogeneity  in  the  vapour  of  acetic  acid, 
we  conclude  that  this  vapour  at  low  temperatures  contains 
molecules,  or  molecular  groups,  the  parts  of  which  hold  to- 
gether throughout  small  temperature-intervals,  and  that  these 
molecules,  or  groups,  are  heavier  than  those  which  compose 
the  vapour  of  the  same  acid  at  temperatures  about  100°  above 
the  boiling  point  of  the  compound1. 

If  we  define  a  molecular  compound,  as,  a  compound  the 
molecules  of  which  may  exist  in  the  gaseous  state  at  low 
temperatures  but  are  gradually  decomposed  into  less  dense 
molecules  of  the  same  kind  of  matter  as  temperature  rises, 
then  we  must  admit  that  at  temperatures  not  far  above  its 
boiling  point  acetic  acid  is  a  molecular  compound. 

But  if  this  is  so,  we  evidently  have  a  series  of  substances, 
beginning  with  solutions  of  salts  or  gases  in  water,  and 
proceeding  through  crystallised  solid  salts  to  acetic  acid 
vapour  at  low  temperatures,  which  connects  mechanical  mix- 
tures on  the  one  hand  with  stable  gaseous  compounds  on  the 
other. 

It  might  be  urged  that  we  ought  not  to  distinguish  be- 
tween the  particles  which  compose  acetic  acid  vapour  at  low 
temperatures  and  those  which  form  the  vapour  of  the  same 
acid  at  high  temperatures ;  that  if  a  molecule  is  '  that  small 
part  of  a  gas  the  parts  of  which  do  not  part  company  when 
the  gas  is  hot,'  then  the  reasoning  which  compels  us  to  say, 
that  the  molecule  of  acetic  acid  vapour  at  220°  is  represented 
by  the  formula  C2H4O2,  likewise  compels  us  to  say,  that  at 
120°  the  molecule  of  this  gas  is  represented  by  the  formula 
C3H6O3.  The  statement  that  acetic  acid  at  low  temperatures 
is  a  molecular  compound  does  net  appear  to  me  to  go  against 

1  Another  explanation  of  the  anomalies  in  the  sp.  gr.  of  acetic  acid  vapour 
has  been  given  by  Horstmann;  it  is  based  on  the  hypothesis  that  the  path  of  a 
molecule  between  two  collisions  is  not  always  a  straight  line.  See  O.  E.  Meyer, 
Die  Kinetische  Theorie  der  Case,  pp.  80,  81. 


§  101]  ATOMIC   AND   MOLECULAR   SYSTEMS.  2O/ 

this  reasoning;  for  this  statement  only  implies  that  at  low 
temperatures  the  vapour  of  this  acid  is  composed  of  particles, 
of  varying  masses, — which  may  be  called  molecules  or  mole- 
cular groups, — but  that  these  all  tend  to  separate  into  particles 
whose  composition  is  represented  by  the  formula  C2H4O2. 
The  C2H4O2  particle  is  stable  throughout  so  large  a  range 
of  temperature  that  we  may  apply  to  it  and  to  it  only  the 
knowledge  we  have  gained  regarding  the  structure  of  mole- 
cules. It  is  better  not  to  apply  the  term  molecule  to  the 
heavier  particles,  (i)  because  they  so  readily  separate  into 
lighter,  and  stable  molecules  ;  (2)  because  what  we  know  of 
molecular  structure  has  been  gained  from,  and  can  therefore 
only  be  strictly  applied  to,  the  study  of  molecules  which  are 
stable  throughout  a  considerable  range  of  temperature  ;  and 
(3)  because  by  recognising  the  possibility  of  the  existence  in 
a  gas  of  groups  of  molecules,  which  are  not  mere  mixtures 
but  on  the  other  hand  are  not  to  be  classed  as  true  molecules, 
we  have  the  means  of  explaining,  in  a  general  way,  many 
phenomena  which  at  present  cannot  be  explained  by  any 
other  equally  simple  hypothesis  which  is  in  keeping  with  the 
fundamental  conceptions  of  the  molecular  theory  of  matter. 

That  the  existence  of  molecular  groups  in  a  gas  at  low  tem- 
peratures is  in  keeping  with  this  theory  can  readily  be  shewn. 
When  two  gases  are  at  equal  temperatures  the  mean  kinetic 
energy  of  agitation  of  the  molecules  must  be  the  same  in 
both ;  but  although  the  mean  kinetic  energy  is  constant  for  a 
given  temperature,  yet  the  kinetic  energy  (and  hence  the 
temperature)  of  many  molecules  may  differ  from  this  mean 
value.  If  the  temperature  of  the  gas  is  increased,  there  is  an 
increase  not  only  of  the  energy  of  agitation  of  the  molecules 
as  a  whole,  but  also  of  the  energy  due  to  the  internal  motions 
of  parts  of  each  molecule  :  as  the  latter  energy  increases,  a 
point  is  reached  at  which  the  molecule  decomposes  into  its 
constituent  parts,  but  these  may  again  unite  in  some  other 
portion  of  the  mass  of  gas.  As  temperature  continues  to  rise 
a  point  will  come  at  which  molecular  decompositions  and  re- 
compositions  are  equal  in  unit  of  time ;  the  temperature  at 
which  this  state  of  matters  is  reached  has  been  called  (by 


208  CHEMICAL   STATICS.  [§  IOI 

Naumann  and  others)  the  decomposition-temperature;  from  this 
point  onwards  the  molecular  decompositions  will  exceed  the 
recompositions,  until  finally  there  are  no  recompositions,  or 
these  are  so  few  in  number  that  the  average  state  of  the 
gas  is  fitly  described  as  that  of  complete  decomposition. 

Now  if  we  suppose  that  the  gas  coming  from  a  liquid  at, 
or  near  to,  its  boiling  point  consists  to  a  great  extent  of 
molecular  aggregations,  we  may  trace  the  gradual  decom- 
position of  these  aggregates  into  true  gaseous  molecules,  just 
as  we  have  traced  the  decomposition  of  molecules  of  one 
kind  of  matter  into  those  of  another  kind  of  matter.  The 
molecular  theory  of  evaporation  and  condensation  almost 
necessitates  the  assumption  that  groups  of  molecules  may 
exist,  and  behave  for  certain  small  changes  in  physical  con- 
ditions, as  definite  wholes :  the  facts  of  spectroscopic  science 
seem  also  to  point  to  a  similar  hypothesis1. 

But  why,  it  might  be  asked,  should  not  all  molecules 
decompose  when  heated  ?  It  is  extremely  probable  that  all 
molecules  are  capable  of  being  decomposed  by  heat.  The 
results  of  recent  experiments  on  iodine  vapour  seem  to  shew 
that  the  diatomic  molecules  of  this  gas  are  separated  into 
atoms  at  high  temperatures.  The  following  table  exhibits 
the  process  of  change  from  I2  to  I. 

Dissociation  of  Iodine  molecules*. 

in        Mean  increase 


Temp.    Sp"  gr  of      ,  *^c""^          *"**  ™          percentage       in  decomposition 
vapour.  lomposiuon.         temp.       decomposition.  for  100°. 


448°  874 

680  8-23 

764  8-28 

855  8-07  8-6,   go 6 

940  7-60     14-5     ;  IOC{ ;   ;  I0.< ;;    ;  I0.2 


1043    7-01     25-05 
1275     5-82    50-5 


232  25*5 iro 


<aK7t  .390    -,7    66,  •    "i  •    '^ ™ 

mate^  (,468         5-06         73-.1  78   69 8 

1  In  connection  with  this  subject  see  especially  the  article  'Constitution  of 
bodies,'  by  Clerk  Maxwell,  in  the  Encyclopedia  Britannica.    (pth  Ed.) 

2  Naumann,  Ber.  13.  1050,  using  the  numbers  of  Crafts  and  Meier,  do.  do. 
868. 


§§  IOI,  102]      ATOMIC   AND   MOLECULAR   SYSTEMS.  209 

Somewhat  similar  results  have  been  obtained  with  bromine. 
A  fact  of  much  interest  is  disclosed  by  studying  the  specific 
gravities  of  bromine  and  chlorine  at  low  and  at  high  tem- 
peratures ;  some  of  the  results  of  such  a  study  are  given  in 
the  following  table1. 

Densities  of  Bromine  and  Chlorine. 

Temp,  measured  in  degrees  above  Qr«>™fi^  r,  Deviation  of  sp.  gr.  from  normal, 

boiling  point  of  in  percentages  of  latter  :— 

BROMINE.    CHLORINE.  BROMINE.        CHLORINE.  BROMINE.     CHLORINE. 


40° 

40° 

57II5 

2-4844 

3-38I 

1-397 

60 

60 

5-6809 

2-4810 

2*872 

I-26l 

80 

80 

5-6503 

2-4776 

2-223 

ri22 

100 

100 

5-6197 

2-4742 

I7I9 

0-984 

120 

120 

5-5891 

2-4708 

1-650 

0-845 

1  60 

1  60 

5-5279 

2-4641 

0^058 

0-571 

20O 

2-4572 

0*290 

240 

2-4504 

O'OOO 

We  have  here  a  phenomenon  very  analogous  to  that  pre- 
sented by  acetic  acid ;  and  if  an  analogous  explanation  is  to 
be  given,  we  must  suppose  that  bromine  vapour  at  tem- 
peratures from  40  to  140  degrees  above  the  boiling  point  of 
this  substance  contains  molecular  groups  which  are  slowly 
decomposed  as  temperature  increases ;  and  that  the  same 
holds  good  of  chlorine  vapour,  only  that  in  this  case  the 
molecular  groups  are  relatively  lighter,  but  more  stable  as 
regards  heat,  than  those  of  bromine. 

Facts  have  now  been  recounted  sufficient  I  think  to 
warrant  the  adoption  of  the  hypothesis  that,  even  in  gases, 
molecules  may  hold  together  in  groups,  the  members  of 
which  do  not  part  company  throughout  more  or  less  ex- 
tended ranges  of  temperature  and  pressure ;  and  if  this  is .  so 
in  gases,  much  more  should  we  expect  it  to  be  so  in  liquids 
and  solids. 

1 02.  The  hypothesis,  by  the  application  of  which  we  hope 
to  find  many  groups  of  facts  falling  into  some  kind  of  order, 
may  be  broadly  stated  as  consisting  in  the  recognition  of  a 
third  order  of  particles  more  complex  than  the  molecule,  as 
the  molecule  is  more  complex  than  the  atom.  This  hypothesis 

1  Jahns,  Ber.  15.  1238. 
M.  C.  14 


210  CHEMICAL   STATICS.  [§  IO2 

affords  no  definition  of  the  third  order  of  particles,  nor  does  it 
always  enable  us  to  refer  a  special  case  to  this  order,  or  to 
that  of  molecules.  It  is  a  general  guide  and  as  such  it 
must  be  employed  ;  if  we  refuse  its  help  we  shall  have  to 
attempt  the  application  of  a  theory,  deduced  solely  from 
considerations  regarding  gases,  to  explain  phenomena  pre- 
sented by  solids  and  liquids ;  how  we  may  hope  to  fare  in 
this  attempt  will  be  sufficiently  indicated  by  a  study  of  those 
ingenious  pictorial  representations  which  are  sometimes  called 
the  structural  formulae  of  mineral  compounds. 

The  properties  of  crystalline  salts  which  more  or  less 
quickly  lose  water  in  vacuo,  and  of  other  solid  salts  which  are 
unstable  under  diminished  pressures,  are  explained  in  a 
general  way  in  terms  of  the  molecular  theory  by  the  aid  of 
the  hypothesis  of  molecular  compounds.  Most  hydrated  salts 
quickly  part  with  'water  of  crystallisation'  in  vacuo,  some 
however  only  slowly ;  some  processes  of  change  proceed  in 
a  vacuum  very  slowly,  e.g.  ammonium  carbamate  is  very 
gradually  changed  into  ammonia  and  carbon  dioxide 
[CO  .  ONH4 .  NH2  =  C02  +  2NHJ. 

Many  salts  when  in  solution  undergo  changes  not  so 
marked  as  those  usually  called  chemical,  and  yet  too  definite 
to  be  altogether  classed  as  physical ;  the  expression  { dis- 
sociation of  salts  in  solution5  is  sometimes  applied  to  these 
processes,  but  the  term  does  not  appear  to  be  well  chosen. 
The  direction  of  the  change  is  reversible  by  altering  the 
condition  of  temperature.  Thus  hydrated  cobalt  chloride 
crystallises  in  a  rose-red  form  (CO2C14 .  I2H2O),  while  the 
colour  of  the  dehydrated  crystals  (CO2C14)  is  blue.  If  an 
aqueous  solution  of  the  red  salt  is  warmed,  the  colour  slowly 
becomes  darker  and  finally  changes  to  blue ;  but  the  rose- 
red  colour  gradually  reappears  as  the  liquid  cools.  The 
temperature  at  which  the  change  from  hydrated  to  dehydrated 
salt  occurs  is  the  lower,  the  less  water  is  present  relatively  to 
the  amount  of  salt.  A  crystal  of  cobalt  chloride  growing  in  a 
blue-coloured  solution  can  be  seen  under  the  microscope  to 
be  surrounded  by  a  film  of  pink  liquid,  which  indicates  the 
existence  round  the  crystal  of  a  zone  of  liquid  containing 


§  102]  ATOMIC   AND   MOLECULAR   SYSTEMS.  211 

relatively  less  of  the  salt  than  the  rest  of  the  solution1. 
The  solubility  of  ordinary  Glauber's  salt  (Na2SO4.  ioH2O) 
in  water  increases  until  the  temperature  of  33° — 34°  is  reached, 
when  crystals  of  the  dehydrated  salt  (Na2SO4)  are  deposited ; 
the  solubility  in  water  of  the  dehydrated  salt  decreases  from 
1 8°  upwards ;  from  these  facts,  and  from  the  results  of  many 
experiments  by  Lowell2,  it  is  almost  certain  that  the  particles, 
the  composition  of  which  is  represented  by  the  formula 
Na2SO4.  ioH2O,  separate  at  33°—  34°,  even  in  presence  of 
water,  into  Na2SO4  and  H2O. 

We  seem  to  be  justified  in  asserting  that  the  solution  of  a 
solid  in  a  liquid,  if  unaccompanied  by  chemical  change  or 
by  formation  of  molecular  groups,  is  always  attended  with 
absorption  of  heat ;  if,  therefore,  heat  is  evolved  during 
solution  we  conclude  that  some  action  other  than  the  mere 
separation  of  the  molecules  of  the  solid  among  those  of 
the  liquid  has  occurred.  Now  if  each  of  the  three  salts, 
Na2HPO4.i2H2O,  Na2HPO4.;H2O  and  Na2HPO4,  is  dis- 
solved in  water  in  such  quantity  that  the  solution  shall 
contain  the  same  relative  amounts  of  Na2HPO4. 12H2O  and 
water,  it  is  found  that  heat  is  absorbed  during  the  solution  of 
the  two  hydrated  salts  and  evolved  during  the  solution  of 
the  dehydrated  salt.  The  following  table  contains  the  details8: 

c_if  Grms.  of  salt        Grms.  of  water  Value  of  thermal 

used*.  t  used4.  change. 

Na2HPO4.  I2H2O  16-35  285  - 1024-98  gram-units. 

Na2HPO4.7H2O  12*25  289*1  -   516-22       „      „ 

Na2HPO4  6-51  294-84  +   249-88       „      „ 

In  the  solution  of  Na2HPO4.7H2O,  less  heat  is  absorbed 
than  in  the  solution  of  the  salt  Na2HPO4. 12H2O;  and  in  the 
solution  of  Na2HPO4  a  considerable  quantity  of  heat  is  evolved. 
These  results  are  at  once  explained  by  saying  that  the  negative 
thermal  change  which  accompanies  the  solution,  pure  and 

1  See  Lehmann,  loc.  cit.  p.  99  :  see  also  Potilitzin,  Ber.  17.  276. 

2  Ann.  Chim.  Phys.  [3]  49.  32.     See  also  Watts's  Diet.  5.  612. 

3  Pfaundler,  Ber.  4.  775. 

4  In  each  case  301-35  grms.  of  solution  is  formed  containing  5-425  per  cent,  of 
Na2HPO4i2H2O.     Specific  heat  of  this  solution  was  constant =0-972. 

14—2 


212 


CHEMICAL  STATICS. 


[§102 


simple,  of  Na2HPO4.  I2H2O  is  partly  balanced  by  the  positive 
thermal  change  accompanying  the  fixation  of  molecules  of 
water  by  the  salt  Na2HPO4.  ;H2O  to  form  Na2HPO4. I2H2O, 
and  is  more  than  balanced  by  the  positive  change  accompany- 
ing the  fixation  of  a  greater  number  of  molecules  of  water 
during  the  solution  of  the  salt  Na2HPO4  also  to  form  the 
salt  Na2HPO4. 12H2O1.  A  saturated  solution  of  any  of  these 
salts  deposits  crystals  of  Na2HPO4.  I2H2O  at  ordinary  tempe- 
ratures. Hence,  from  these  data,  we  conclude  that  a  solution 
of  sodium  phosphate  most  probably  contains  particles  whose 
composition  is  represented  by  the  formula  Na2HPO4.  12 H2O 
(and  it  may  be  some  particles,  Na2HPO47H2O  or  5H2O)  but 
inasmuch  as  the  composition  of  these  particles  very  readily 
undergoes  change,  we  prefer  to  call  them  molecular  groups 
rather  than  molecules. 

The  thermal  phenomena  attending  the  solution  in  water  of 
many  other  salts,  as  presented  in  the  following  table  (taken 
from  Naumann's  book),  are  readily  explained  by  assuming 
that  each  solution  contains  molecular  groups  of  somewhat 

Values  of  thermal  changes  attending  solution  in  water  of  -various 

sulphates. 

Gram-units  of  heat  evolved  or  absorbed  during  solution  of 


Amount  01 
salt 

dehydrated 

salt 

salt 

salt 

salt 

salt 

employed. 

salt 

with  iH2O 

with  3H2O 

with  5H2O 

with  7H2O 

with  ioH2O 

MgS04 

20,304  + 

10,986  + 

2388- 

3720- 

ZnSO4 

18,578  + 

9,624  + 

2332- 

4148- 

CuSO4 

16,298  + 

9,468  + 

2432- 

4260- 

MnSO4 

14,170  + 

8,432  + 

470  + 

CdSO4 

10,688  + 

6,020  + 

3,062  + 

Na2SO4 

708  + 

18,600- 

(NH4)2S04    1950- 
K2SO4  6340- 

1  Calculations  based  on  this  assumption,  using  Pfaundler's  numbers,  give  the 
following  result  [Naumann,  Ueber  Molekiilverbindungen  nach  festen  Verhdltnissen, 
p.  41]: 

The  change,  Na2HPO4+  i2H2O  =  Na2HPO4.  i2H2O  is  accompanied  by  evolu- 
tion of  27,892  gram-units  of  heat. 

The  change,  Na2HPO4+  7H2O  =  Na2HPO4 .  7H2O  is  accompanied  by  evolu- 
tion of  16,744  gram-units  of  heat. 

The  change,  Na2HPO4+  5lI2O  =  Na2HPO4 .  sHoO  is  accompanied  by  evolu- 
tion of  11,148  gram-units  of  heat. 


§  102]  ATOMIC   AND   MOLECULAR  SYSTEMS.  213 

varying  composition,  and  that  that  group,  the  formation  of 
which  is  attended  with  the  greatest  loss  of  energy  (as  mea- 
sured by  heat  evolved)  is  present  in  largest  quantity  in  a 
solution  in  much  water. 

The  separation  of  a  solid  from  solution  in  a  liquid  must 
be  attended  with  evolution  of  heat.  If  reactions  between  salts 
which  form  no  molecular  compounds  (or  only  very  unstable 
compounds)  with  water  at  ordinary  temperatures,  are  compared 
with  reactions  wherein  salts  which  form  comparatively  stable 
molecular  compounds  with  water  are  concerned,  precipitates 
being  produced  in  both  cases,  it  is  found  that  whereas  the 
former  reactions  are  accompanied  by  evolution,  the  latter  are 
rather  marked  by  absorption  of  heat.  Thus,  partly  from  the 
large  negative  values  of  the  thermal  change  accompanying  the 
solution  in  water  of  PbCl2,  Pb.2NO3,  NaCl,  and  NaNO3,  and 
partly  from  the  fact  that  solutions  of  these  salts  deposit 
crystals  of  the  dehydrated  salts  at  ordinary  temperatures,  we 
may  conclude  that  the  solutions  in  question  contain  either  the 
dehydrated  salts  or  very  unstable  molecular  compounds  of 
these  salts  with  water :  on  the  other  hand  aqueous  solutions  of 
K2CO3,  Na2CO3,  MgSO4  almost  certainly  contain  comparatively 
stable  groups  of  molecules,  composed  of  molecules  of  these 
salts  and  of  water. 

The  following  numbers  represent  the  values  of  the  thermal 
changes  which  accompany  the  formation  of  some  solid  salts. 
(The  formula  represents  quantity  of  salt  in  grams  in  the 
solution  used.) 

Thermal  value  of  change. 
Pb    2ND  Gram-units. 

- 2         (in  2  litres  of  water) +  NaCl  (in  2  litres) 

yields  solid  PbCl2        ...     1530+. 

CaCl2     ,  K2CO3    .  . , 

2    H 3  yields  solid  CaCO3          450-. 


MgS04+K£0,          .  MgCQj        io5Q_ 


2  2 


It  seems,  from  these  numbers,  that  the  heat  absorbed  in 
decomposing   the    molecular   compounds   of  CaCl2,    K2CO8, 


214  CHEMICAL  STATICS.  [§  IO2 

Na2CO3,  and  MgSO4  with  water,  is  greater  than  that  evolved 
in  the  formation,  and  separation  from  solutions,  of  solid  CaCO3 
or  MgCO3. 

Granting  then  that  the  evolution,  or  absorption,  of  heat 
noticed  during  solution  of  a  salt  in  water  is  to  be  traced 
in  part  to  the  formation,  or  non-formation,  of  complex 
groups  of  molecules,  it  follows  from  all  we  know  concerning 
such  groups  that  the  fact  that  the  solution  of  a  dehydrated 
salt  is  attended  with  absorption  of  heat  does  not  of  itself  prove 
the  non-formation  of  groups  consisting  of  molecules  of  the 
salt  and  water.  Molecular  compounds  ought  to  shew  a  wide 
range  of  stability,  graduating  off  on  the  one  side  into  true 
compounds  and  on  the  other  into  mixtures.  Among  the 
conditions  favourable  or  otherwise  to  the  fixation  of  molecules 
of  water  by  molecules  of  a  salt  dissolved  therein  we  should 
regard  temperature  as  very  important.  A  withdrawal  of  heat 
from  a  strong  solution  might  induce  such  sluggishness  of 
molecular  movements  as  would  result  in  the  formation  of 
molecular  groups. 

Guthrie1  found  that  when  a  strong  aqueous  solution  of 
common  salt  is  cooled  below  o°  it  deposits  crystals  having 
the  composition  NaC1.2H2O,  and  that  at  —21°  the  whole 
liquid  sets  into  a  mass  of  crystals  containing  salt  and  water  in 
the  proportion  expressed  by  the  formula  2NaCl .  2iH2O. 

Many  cryohydrates  of  other  salts  have  been  prepared  by 
Guthrie,  e.g. 

Formula.  Solidifying  point. 

NH4Cl.i2H2O  -15° 

MgSO4.24H2O  -6° 

Na2SO4.  i66H2O  -07° 

KC1O3.222H2O  -0-5° 

K2Cr2O7.292H2O  - 1° 

KMnO4.6o8H2O  -0-37° 

SrO.i463H2O  -o'i° 

Each  cryohydrate  is  characterised  by  definite  melting 
and  solidifying  points  and  definite  crystalline  form ;  but  above 

1  Phil  Mag.  [4]  49.  i  and  206;  [5]  1.  49,  354,  446;  2.  212;  6.  35,  105.  For 
a  description  of  some  alcoholates,  e.g.  MgCl26C2H5OH,  see  Simon,  J.  pract. 
Chemie(2)  20.  371. 


§  102]  ATOMIC  AND   MOLECULAR   SYSTEMS.  21  5 

a  certain  (low)  temperature  each  separates  into  molecules  of 
water  and  salt,  or  of  water  and  hydrated  salt.  The  properties, 
and  the  phenomena  attending  the  formation,  of  cryohydrates, 
are  evidently  in  keeping  with  the  special  phase  of  the  mo- 
lecular theory  which  we  are  now  considering1. 

From  the  results  of  Lehmann's  microscopic  studies2  on 
the  formation  of  crystals  of  hydrated  ferrous  chloride,  cobaltous 
chloride,  and  cupric  chloride  it  appears  certain  that  a  solution 
from  which  crystals,  now  of  a  more  hydrated  now  of  a  less 
hydrated  salt,  separate,  as  temperature  varies,  does  not  contain 
at  a  fixed  temperature  only  the  one  hydrate  and  at  another 
temperature  only  the  other  hydrate.  As  temperature  slowly 
rises  the  molecular  groups  tend  to  fall  in  pieces  and  so 
the  liquid  becomes  poorer  in  particles  of  the  relatively  most 
hydrated  salt;  on  cooling,  the  conditions  are  reversed,  and 
the  liquid  becomes  poorer  in  particles  of  the  least  hydrated 
salt.  Lehmann  considers  the  three  cases  (i)  the  liquid  is 
equally  saturated  for  the  hydrate  rich  in  water  and  for  that 
poorer  in  water;  (2)  the  liquid  contains  rather  more  of 
one  hydrate  than  of  the  other;  (3)  the  liquid  is  con- 
centrated as  regards  one  hydrate,  but  dilute  as  regards  the 
other.  He  shews  that,  as  temperature  slowly  increases,  in  the 
first  case,  crystals  of  both  hydrates  grow  simultaneously  and 
at  the  same  rate  until  the  spheres3  of  the  crystals  touch,  when 
growth  is  almost  entirely  stopped;  in  the  second  case,  both 
kinds  of  crystals  grow,  but  one  kind  more  quickly  than  the 
other,  then  both  grow  at  the  same  rate,  and  then  the  second 
kind  of  crystals  grow  more  rapidly  than  the  first ;  in  the  third 


1  The  hypothesis  of  the  formation  at  low  temperatures  of  complex  unstable 
molecular  groups  helps  us  to  understand  some  of  the  phenomena  presented  by 
variations  in  the  rate  of  chemical  changes  under  abnormal  circumstances;    this 
subject  will  be  considered  in  the  second  part  of  this  work.     The  same  hypothesis 
also  throws  light  on  the  action  of  concentrated  and  dilute  hydrochloric  acid  on 
antimony  sulphide :  this  is  fully  considered  under  '  Thermal  Chemistry, '  see  post, 
chap.  iv.  section  1. 

2  Loc.  cit.  pp.  100 — 103. 

3  Lehmann's  term  is  'der  Hof  des  Krystalles:'  each  crystal,  he  says,  can  be 
seen  under  the  microscope  to  be  surrounded  by  a  liquid  film,  from  which  it  draws 
its  supplies  of  solid  matter ;  this  is  the  Hof  or  sphere  of  the  crystal. 


2l6  CHEMICAL   STATICS.  [§  IO2 

case,  those  crystals  which  are  present  in  the  liquid  in  greater 
quantity  grow  rapidly,  and  the  others  dissolve  rapidly,  so 
that  the  dissolving  crystals  appear  to  pass  directly  into  crystals 
of  the  other  hydrate. 

The  definite  form,  solubility,  temperature  of  formation,  &c. 
of  each  kind  of  crystal  formed  in  these  experiments  conducted 
by  Lehmann  prevent  us  from  regarding  the  various  hydrated 
salts  as  mere  mixtures  of  ice  and  salt ;  on  the  other  hand,  the 
extremely  small  variations  in  temperature,  or  relative  amount 
of  water  and  salt,  necessary  to  cause  change  from  one  crystal 
to  another,  equally  prevent  us  from  attempting  to  explain  the 
properties  of  each  hydrate  as  wholly,  or  almost  wholly,  con- 
ditioned by  the  mutual  interactions  of  atoms  within  the 
molecule:  we  seem  forced  to  adopt  the  hypothesis  of  molecular 
compounds. 

The  researches  of  Graham  on  colloidal  and  crystalloidal 
substances  are  of  the  utmost  importance  as  regards  the 
hypothesis  we  are  considering;  to  understand  the  importance 
of  Graham's  work  it  is  necessary  carefully  to  study  the  whole 
series  of  papers  on  liquid  diffusion  which  he  communicated  to 
the  Royal  Society1.  Graham2  found  that  certain  substances 
when  in  solution  pass  very  quickly  through  wet  animal  or  vege- 
table membranes,  while  others  are  scarcely,  if  at  all,  diffusible 
through  the  same  septa.  The  more  diffusible  bodies  Graham 
called  cystalloids,  the  less  diffusible  he  called  colloids.  Colloidal 
substances  e.g.  albumen,  hydrated  alumina  or  stannic  oxide, 
&c.  are  very  inert  chemically  considered,  but  at  the  same 
time  they  are  affected  by  the  smallest  changes  in  their  en- 
vironment e.g.  slight  alterations  of  temperature  cause  marked 
changes  in  their  properties;  they  are  easily  permeated  by 
diffusible  crystalloidal  substances,  to  which,  says  Graham, 
they  give  up  water,  ' molecule  by  molecule';  'their  existence 
'is  a  continual  metastasis'.  Ice,  which  under  ordinary  con- 
ditions of  formation  is  crystalloidal,  when  formed  in  contact 
with  water  at  o°  possesses  those  properties  which  characterise 

1  Happily  Graham's  papers  have  been  collected  and   published  by  the  late 
Drs  Angus  Smith  and  James  Young. 

2  Phil.  Trans,  for  1861,  185. 


§  102]  ATOMIC   AND    MOLECULAR    SYSTEMS.  2 1/ 

colloids;  'can  any  facts  more  strikingly  illustrate  the  maxim 
'that  in  nature  there  are  no  abrupt  transitions,  and  that 
'distinctions  of  class  are  never  absolute?'  (Graham). 

The  marked  differences  between  the  properties  of  colloids 
and  crystalloids  are  associated,  in  the  opinion  of  Graham,  with 
differences  of  molecular  structure.  He  regarded  the  reacting 
unit  of  a  colloid  as  probably  formed  by  the  coalescence  of  a 
large  number  of  molecules,  hence  the  marked  instability,  and 
at  the  same  time  chemical  inertness,  which  characterise  the 
class  of  colloidal  substances. 

Some  very  interesting  observations  have  been  made  by 
van  Bemmelen1  on  the  absorption  of  acids  and  salts  by 
hydrated  oxides.  When  the  hydrated  dioxide  of  tin,  silicon, 
or  manganese  is  shaken  with  an  aqueous  solution  of  a 
mineral  acid,  or  a  salt  such  as  potassium  sulphate  or  sodium 
chloride,  a  definite  quantity  of  the  acid  or  salt  is  absorbed  by 
the  oxide ;  the  amount  absorbed  is  dependent  on  the  nature 
of  the  hydrated  oxide  and  the  nature  of  the  acid  or  salt, 
on  the  relative  masses  of  oxide,  acid,  or  salt,  and  on  the 
amount  of  water  present.  The  substances  which  exhibit  this 
action  are  characterised  by  the  readiness  with  which  the 
change  from  hydrated  to  dehydrated  salt  and  vice  versa 
occurs  ;  thus  the  hydrates  SnO2 .  ^H2O,  SiO2 .  *H2O,  and 
MnO2.;rH2O  part  -with  water  when  placed  over  sulphuric 
acid,  and  the  oxides  absorb  water  when  placed  in  a  moist 
atmosphere.  The  amount  of  water  absorbed  by  any  one  of  the 
dehydrated  oxides  depends  in  part  on  its  physical  state ;  if 
the  oxide  is  strongly  heated  it  absorbs  less  water  than  if  dried 
over  sulphuric  acid  in  vacuo* ;  the  '  looser '  the  aggregation  of 
the  particles,  the  greater  the  quantity  of  water  absorbed  by 
the  oxide. 

In  some  cases,  e.g.  the  hydrate  SiO2.4H2O,  the  amount 
of  acid  or  salt  withdrawn  from  an  aqueous  solution  was 

1  J.  fiir  prakt.  Chemie  [2]  23.  324  ;  see  also  26.  227. 

2  Graham  {Brit.  Ass.  Reports  for  1834,  579]  called  attention  to  the  difference 
between  strongly  heated  calcium  sulphate  and  the  same  substance  'in  a  state  for 
setting:'  but,  says  Graham,  "this  is  a  department  of  corpuscular  philosophy  which 
stands  much  in  want  of  further  development." 


218  CHEMICAL   STATICS/  [§  IO2 

found  to  be  equivalent  to  the  amount  of  water  loosely  held 
by  the  oxide,  i.e.  the  water  removed  by  drying  over 
sulphuric  acid  in  vacua.  In  other  cases,  e.g.  SnO2.3H2O, 
Sn02.2-3H20,  Sn02.r5H20,  MnO2.2'5H2O,  MnO2.2H2O, 
the  amount  of  salt,  &c.,  withdrawn  by  the  hydrate  from  solu- 
tion was  greater  than  the  quantity  equivalent  to  the  loosely- 
held  water  of  the  hydrate.  As  the  amount  of  water  which  an 
oxide  absorbs  from  a  moist  atmosphere  was  found  to  vary 
with  the  physical  aggregation  of  that  oxide,  so  the  amount 
of  salt  or  acid  absorbed  by  the  hydrated  oxide  was  found 
to  shew  analogous  variations :  this  is  specially  worked  out 
in  detail  by  van  Bemmelen  for  the  action  of  metastannic 
acid  on  aqueous  solutions  of  HC1,  H2SO4,  KC1,  K2SO4, 
and  KNO8. 

If  these  actions  are  to  be  classed  as  purely  physical,  we 
should  not  expect  to  find  a  definite  limit  to  the  amount  of 
salt  or  acid  absorbed  by  each  hydrated  oxide ;  but  van  Bem- 
melen's  researches  shew  that  the  process  tends  to  the  esta- 
blishment of  an  equilibrium  between  acid  (or  salt),  water,  and 
hydrated  oxide,  that  this  condition  is  attained  slowly,  and  that 
it  is  affected  by  the  relative  masses  of  the  acting  substances  in 
the  original  system.  Thus  less  acid  (or  salt)  is  absorbed  from 
a  very  dilute  than  from  a  more  concentrated  solution,  but  the 
amount  of  acid,  &c.,  absorbed  increases  much  more  slowly 
than  the  increase  in  the  concentration  of  the  solution  of  acid 
or  salt.  The  final  equilibrium  is  not  disturbed  by  addition  of 
more  acid  (or  salt)  solution  of  the  same  degree  of  concentra- 
tion as  that  surrounding  the  hydrated  dioxide,  but  if  the 
added  solution  is  relatively  richer  in  acid  or  salt  than  the 
liquid  surrounding  the  dioxide,  then  the  equilibrium  is 
overthrown  and  the  absorption  of  acid,  &c.,  begins  again 
and  proceeds  till  a  second  condition  of  equilibrium  is  es- 
tablished. 

Some  hydrated  oxides  not  only  absorb,  but  also  partially 
decompose  salts:  e.g.  MnO2. 2-5 H2O  when  shaken  with  an 
aqueous  solution  of  K2SO4  absorbs  a  definite  amount  of  the 
latter  and  at  the  same  time  separates  part  of  it  into  KOH 
and  H2SO4.  Again,  one  salt  is  sometimes  absorbed  in  pre- 


§§  IO2,  103]     ATOMIC  AND   MOLECULAR   SYSTEMS.  2IQ 

ference  to  another,  thus  if  MnO2.;rH2O  is  shaken  in  contact 
with  H2SO4,  washed,  and  again  shaken  in  contact  with  an 
aqueous  solution  of  K2SO4,  a  portion  of  the  H2SO4  which  had 
been  absorbed  by  the  hydrated  oxide  is  replaced  by  K2SO4 ; 
again,  if  SiO2.4H2O  is  allowed  to  absorb  A12C16,  is  then 
washed  till  the  washings  no  longer  contain  chlorine,  and  is . 
finally  shaken  with  an  aqueous  solution  of  KC1,  it  is  found 
that  some  of  the  KC1  has  been  absorbed  and  some  of  the 
A12C16  has  passed  into  the  surrounding  liquid. 

These  substances,  investigated  by  van  Bemmelen,  whether 
they.be  called  compounds  or  loose  combinations  of  salt  (or 
acid)  and  hydrated  oxide,  can  scarcely  be  regarded  as  com- 
posed of  molecules  each  built  up  of  atoms  of  metal,  oxygen, 
hydrogen,  and  the  elements  of  acid  or  salt,  but  rather  as 
composed  of  molecular  groups  each  constituted  by  the  co- 
alescence of  molecules  of  acid  (or  salt),  water,  and  metallic 
oxide,  the  number  of  such  molecules  in  each  group  or  (  re- 
'  acting  unit'  being  variable  within  certain  limits.  The  pro- 
perties of  many  of  the  salts  of  the  'weaker'  acids — e.g. 
carbonic,  boric,  and  sulphurous — are  regarded  by  van  Bem- 
melen as  explicable  in  terms  of  the  general  hypothesis  of 
molecular  compounds ;  he  would  regard  the  reacting  units 
of  these  salts  as  molecular  groups,  more  stable  than  those 
which  compose  the  peculiar  class  of  bodies  just  described, 
but  less  stable  than  the  true  chemical  molecule. 

103.  In  his  second  paper  (loc.  cit.)  van  Bemmelen 
has  more  particularly  studied  hydrated  beryllium  oxide 
BeO  .^rH2O.  He  shews  that  two  varieties  of  this  oxide  exist, 
viz.  a  gelatinous  and  a  granular  form,  that  the  former  alone 
exhibits  the  property  of  absorbing  acids  and  salts  from  aque- 
ous solutions,  and  also  that  the  action  of  heat  on  the  two  hy- 
drates is  different.  After  heating  to  220°  the  granular  hydrate 
has  lost  O'5  H2O,  and  is  now  much  altered  in  properties.  This 
fact — and  others  analogous  to  this  are  known — seems  to  shew 
that  by  the  application  of  energy  from  without  the  system  the 
parts  of  a  loose  molecular  group  may  be  caused  to  react  so  as 
to  bring  about  a  marked  change  in  the  properties  of  the  body 
composed  of  such  groups.  In  other  words,  the  comparative 


220  CHEMICAL   STATICS.  [§  103 

readiness  with  which  definite  chemical  changes  may  be  started 
among  the  constituents  of  a  molecular  group  appears  to  shew 
that  although  these  constituents  are  held  together  but  loosely, 
nevertheless  they  are  not  merely  mixed.  Thus,  As(CH3)2Cl 
combines  with  C12  to  form  As(CH3)2Cl3;  when  this  compound 
is  heated  it  yields  As(CH3)Cl2  +  CH3C1 ;  then  As(CH3)Cl2 
readily  takes  up  C12  to  form  As(CH3)Cl4,  which  on  being 
heated  separates  into  AsCl3-f  CH3C1.  Now  on  account  of 
their  properties  some  of  these  compounds  must  be  classed  as 
molecular,  yet  under  the  influence  of  heat  the  parts  of  the 
molecular  groups  mutually  act  and  react  in  a  way  analo- 
gous to,  if  not  identical  with,  that  characteristic  of  chemical 
change.  But  such  phenomena  as  these  are  exactly  what 
might  be  expected  from  the  hypothesis  of  molecular  com- 
pounds ;  if  these  bodies  are  formed  of  groups  of  molecules 
we  should  expect  that  reactions  between  these  groups 
would,  in  many  cases,  easily  occur  and  result  in  the  produc- 
tion of  new,  less  complex,  groups,  or,  it  may  be,  new  molecules. 
That  a  substance  is  found  to  behave  in  a  definite  manner 
under  the  influence  of  this  or  that  reagent  cannot  be  regarded 
as  sufficient  evidence  for  classing  it  among  atomic  rather  than 
molecular  compounds.  Thus  the  observation  recorded  by 
R.  W.  Atkinson1  regarding  the  identity  of  the  salts  produced 
by  mixing  SbCl3  and  3KBr,  and  SbBr3  and  3KC1,'  cannot  be 
regarded  as  proving  that  the  product  of  these  actions  is  built 
up  of  molecules  represented  by  the  formula  ;zSbd3Br3K3,  the 
properties  of  which  are  conditioned  only  by  the  mutual  inter- 
actions of  the  atoms  Sb,  Cl,  Br,  and  K.  Regarded  however 
as  a  contribution  towards  solving  the  questions  suggested  by 
the  term  molecular  compounds,  the  observations  made  by 
Atkinson  are  of  interest,  as  shewing  how  possible  it  is  to  obtain 
substances  which  behave  in  some  respects  as  molecular  and 
in  other  respects  as  atomic  compounds.  It  cannot  be  too 
strongly  insisted  on  that  no  hypothesis  has  been  proposed 
regarding  molecular  compounds  which  furnishes  us  with  a 
definition  of  the  class  'molecular',  or  puts  into  our  hands 

1  C.  S.  Jotirnal,  Trans,  for  1883.  289. 


§  103]  ATOMIC  AND   MOLECULAR   SYSTEMS.  221 

an  instrument  for  determining  whether  a  given  compound 
belongs  to  this  class  or  to  the  class  of  atomic  compounds. 
What  the  hypothesis  does  is  to  negative  the  notion  that  the 
properties  of  all  compounds  are  to  be  explained  by  the  con- 
ception of  actions  and  reactions  between  atoms  which  to- 
gether constitute  a  molecule,  to  restrict  the  application  of 
the  theory  of  valency  to  gaseous  compounds,  and  to  open 
a  path  for  future  research  by  insisting  on  the  complexity  of 
chemical  phenomena,  and  the  folly  of  attempting  to  explain 
all  in  terms  of  a  favourite  theory. 

But  the  consideration  of  molecular  compounds  leads  to 
the  discussion  of  questions  which  properly  belong  to  chemical 
kinetics ;  we  cannot  separate  these  bodies  from  their  environ- 
ment; they  are  members  of  a  system  which  is  continually 
undergoing  change  and  the  comparative  stability  of  which  is 
the  result  of  never  ceasing  action  and  reaction  between  its 
parts.  Chemistry  is  not  a  collection  of  facts  regarding  the 
crystalline  form,  melting  points,  boiling  points,  specific 
gravities,  &c.,  &c.,  of  so-called  pure  elements  or  compounds; 
it  is  rather  the  orderly  and  regulated  study  of  the  changes 
which  matter  undergoes  and  which  result  in  more  or  less 
profound  modifications  in  the  properties  of  the  changing 
bodies. 

A  great  advance  has  certainly  been  made  by  replacing  the 
conception  of  a  molecule  as  an  undefined  quantity  of  matter 
constructed  of  groups  of  atoms  more  or  less  loosely  and 
vaguely  arranged,  by  that  conception  of  the  molecule  which 
regards  it  as  a  definite  and  definable  quantity  of  matter,  built 
up  of  atoms  arranged  in  an  orderly  manner,  and  exhibiting 
functions  dependent  on  the  nature,  arrangement,  and  mutual 
interactions  of  these  atoms.  Among  the  functions  of  these 
molecules  we  must  however,  I  think,  place  the  power  of 
combining  with  other  molecules  to  form  more  or  less  complex 
groups,  less  stable  than  the  molecules  of  a  gas,  and  not  so 
sharply  defined  from  other  groups  as  the  molecule  of  one  com- 
pound is  from  that  of  another.  '  Although  the  explanation  of 
the  properties  of  molecular  compounds  is  not  to  be  brought 
within  the  scope  of  the  theory  of  valency,  nevertheless  if  we 


222  CHEMICAL  STATICS.  [§  IO3 

regard  the  formation  (or  nonformation),  and  the  relative 
stabilities,  of  such  compounds  as  functions  of  all  the  molecules 
concerned  in  their  synthesis,  we  can  see  that  the  valencies 
of  the  elementary  atoms  must  be  important  factors  in  deter- 
mining the  production  of  molecular  compounds1. 

1  In  connection   with  this  subject  compare  van't  Hoff's  Ansichten  iiber  die 
Organische  Chemie,  pp.  4,  5. 


CHAPTER  III. 

THE   PERIODIC   LAW. 

104.  ATTEMPTS  have  from  time  to  time  been  made 
throughout  the  preceding  50  or  60  years  to  trace  connections 
between  the  atomic  weights  and  the  general  properties  of 
groups  of  elements. 

Soon  after  the  appearance  of  Dalton's  New  System  of 
Chemical  Philosophy,  an  hypothesis  was  promulgated  by 
Prout  to  the  effect  that  the  atomic  weights  of  the  elements 
are  whole  multiples  of  that  of  hydrogen;  but  the  researches 
of  Berzelius,  Marignac  and  Stas  shewed  that  this  hypothesis 
was  untenable.  A  modification  of  Prout's  hypothesis  was 
made  by  Dumas  which  appears  to  have  a  fair  probability  in 
its  favour. 

Gmelin,  Dumas,  Gladstone,  Cooke,  Kremers,  Pettenkofer, 
Odling,  and  especially  Newlands1  (who  was  among  the  earliest 
workers  in  this  field,)  have  drawn  attention  to  points  of 
connection  between  the  properties  and  the  atomic  weights  of 
elements. 

It  is  however  especially  to  Mendelejeff2  that  we  owe  the 
systematic  correlation  of  the  atomic  weights  with  the  chemical 
and  physical  properties  of  the  elements. 

Lothar  Meyer3  has  also  made  important  contributions  to 
the  same  subject,  and  in  his  Modernen  Theorien  he  has 

1  Chem.  News,  7.  70,  and  10.  59,  94. 12.  83,  94.  13.  113.  &c.     Newlands'  con- 
tributions to  this  subject  have  been  gathered  together  and  published  in  a  small 
volume  entitled  '  On  the  Discovery  of  the  Periodic  Law'  [Spon.  1884]. 

2  Annalen,  Suppl.  Bd.  8.  133.     See  also  Chem.  News,  Vols.  40  and  41. 

3  Annalen,  Suppl.  Bd.  5.  129,  and  7.  354  &c. 


224  CHEMICAL   STATICS.  [§  10$ 

gathered  together  the  more  important  facts  which  have  been 
established  concerning  the  relation  in  question. 

105.  We  may  confidently  say  that  a  large  probability  has 
been  established  in  favour  of  the  hypothesis  that  the  properties 
of  the  elements,  and  of  the  compounds  of  each  element,  are 
periodic  functions  of  the  atomic  weights  of  the  elements. 
Lothar  Meyer  puts  the  general  statement  of  the  "Periodic 
"Law"  in  this  form1;  'if  the  elements  are  arranged  in  order  of 
'increasing  atomic  weights,  the  properties  of  these  elements 
'vary  from  member  to  member  of  the  series,  but  return  more 
'or  less  nearly  to  the  same  value  at  certain  fixed  points  in 
'the  series'. 

Let  the  elements  be  arranged  in  the  order  of  their  atomic 
weights;  let  this  list  of  elements  be  (broadly)  divided  into 
series  of  sevens;  let  the  members  of  the  second  series  be 
placed  under  those  of  the  first,  those  of  the  third  under  those 
of  the  second,  and  so  on ;  and  let  the  elements  contained  in  a 
vertical  column  be  called  a  group,  those  in  a  horizontal 
column  being  called  a  series.  Then  taking  an  element  R,  and 
calling  the  elements  next  before  and  after  it  in  the  same 
series  X  and  Y  respectively,  and  those  in  corresponding 
positions  in  the  same  group  R'  and  R",  we  may  say  that 

atomic  weight,  density,  and  atomic  volume  of  R= 

atomic  wt.,  density,  atomic  vol.  of  X  +  the  values  of  same  constants  for  Y 

2 
and  also  that  atomic  weight,  &c.  of  R  = 

atomic  weight,  &c.  of  R'  +  constants  of  R" 
2 

In  the  arrangement  of  the  elements  just  described,  each 
group  corresponds,  for  the  most  part,  with  a  natural  family. 
This  is  more  clearly  shewn,  and  the  relations  between  the  atomic 
weights  and  the  properties  of  the  elements  are  more  distinctly 
developed  if  certain  gaps  are  supposed  to  exist  -in  the  list  of 
elements.  The  following  table2  exhibits  this  arrangement  of 
the  elements. 

1  Die  Modernen  Theorien,  4th  Ed.  p.  136. 

2  Taken  from  a  paper  by  B.  Brauner  in  C.  S.  Journal  Trans,  for  1882.    78: 
atomic  weights  are  stated  in  round  numbers. 


THE   PERIODIC   LAW. 


225 


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226  CHEMICAL  STATICS.  [§§  106,  10? 

1 06.  Before  giving  a  detailed  explanation  of  this  table 
let  us  meanwhile  gather  together  some  of  the  best  established 
generalisations   concerning  the   periodic   connection  of  pro- 
perties and  atomic  weights  of  the  elements. 

A  phenomenon  is  said  to  be  periodic  when,  if  the  con- 
ditioning circumstances  vary  continuously,  it  repeats  itself  at 
definite  intervals.  The  variable  under  consideration  is  the 
atomic  weight,  the  phenomenon  to  be  examined  is  the  nature 
of  the  chemical  element  and  its  compounds.  Although  it  is  not 
as  yet  possible  to  state  quantitatively  the  nature  of  the  periodic 
function  which  connects  the  atomic  weights  and  general  pro- 
perties of  the  elements,  it  may  nevertheless  be  established 
that  the  function  in  question  is  periodic.  For  this  purpose 
it  will  be  necessary  to  break  up  the  phenomenon  '  nature 
of  the  chemical  element  and  its  compounds'  and  to  endea- 
vour to  shew  that  the  malleability,  ductility,  atomic  volume, 
power  of  forming  oxides  (or  chlorides)  of  definite  compo- 
sition, position  in  electrical  series,  &c.  of  the  elements  do 
vary  periodically  with  variations  in  the  atomic  weights  of 
these  elements1. 

107.  Atomic  volume.     The  quotient  obtained  by  dividing 
the  specific  gravity  of  an  element,  in  the  solid  form,  by  its 
atomic  weight  is  called  the  atomic  volume  of  that  element. 
This  quotient  expresses  the  volume,   in   cubic   centimetres, 
occupied  by  an  amount  of  the  solid  element,  in  grams,  pro- 
portional to  the  atomic  weight  of  that  element. 

Arranging  the  elements  in  order  of  increasing  atomic 
weights  it  is  found  that  the  value  for  atomic  volume  reaches 
its  first  maximum  at  lithium,  that  it  then  diminishes  through 
beryllium,  boron,  &c.  and  again  increases  through  carbon,  &c. 
reaching  a  second  maximum  at  sodium;  the  other  maxima 
occur  at  potassium,  rubidium,  and  caesium. 

The  periodic  nature  of  the  connection  between  atomic 
volumes  and  atomic  weights  becomes  very  apparent  when  the 

1  For  greater  details  on  this,  point  see  L.  Meyer,  Die  Modernen  Theorien, 
4th  Ed.  pp.  139 — 173,  of  which  this  and  the  few  following  pages  must  be  regarded 
as  an  abstract. 


710      20      30     40     50     60      70 


80  90  100  110  120  130  140  150  160  170 
Thick,  Une  curve  shews  atomic  volumes. 
"JJdrv  „  „  „  mtdtifig  points. 

THESE  POINTS  SHOULD  BE  PLACED    66   DIVISIONS  HIGHER. 


180    200    210    220    230 


§  IO/]  THE   PERIODIC   LAW.  22/ 

magnitudes  of  those  quantities  are  graphically  represented  as 
is  done  on  the  plate  facing  this  page  \ 

The  maximum  points  on  the  curve  are  seen  to  be  occupied 
by  metals  of  low  specific  gravity,  while  the  minimum  points 
are  occupied  by  heavy  metals. 

The  position  of  an  element  on  the  curve,  with  reference  to 
the  preceding  and  succeeding  elements,  appears  to  exert  a 
marked  influence  on  the  properties  of  the  element  in  question. 
Thus  phosphorus  and  magnesium  on  the  one  hand,  and  calcium 
and  chlorine  on  the  other,  have  nearly  equal  atomic  volumes; 
phosphorus  and  chlorine  are  followed  by  elements  the  atomic 
volumes  of  which  are  larger  than  their  own  (i.e.  are  situated 
on  ascending  portions  of  the  curve),  whereas  magnesium  and 
calcium  are  followed  by  elements  having  atomic  volumes 
smaller  than  their  own  (i.e.  are  situated  on  descending  portions 
of  the  curve). 

The  ductile  metals  are  placed  at  or  near  to  maximum  and 
minimum  points  on  the  curve;  those  of  low  specific  gravity 
occurring  at,  and  immediately  after  maximum  points,  and  those 
of  high  specific  gravity  at,  and  immediately  after  minimum 
points.  The  brittle  heavy  metals  occur  in  sections  4,  5?  and  7 
immediately  before  the  minimum  points 2. 

The  elements  on  the  descending  parts  of  sections  2  and  3  of 
the  atomic  volume  curve  are  electropositive  and  form  basic 
hydroxides;  those  on  the  ascending  portions  of  the  same 
sections  are  electronegative  and  form  acid  hydroxides.  Sec- 
tions 4  and  5  each  contain  four  groups  of  elements  arranged  in 
accordance  with  their  negative  or  positive  character.  Electro- 
positive elements  occur  on  the  first  portions  of  the  descending 
curve  in  each  of  these  sections  (K,  Ca;  Rb,  Sr);  these  arc 

1  Only  those  elements  the  specific  gravities  of  which  in  the  solid  state  have 
been  directly  determined  are  included  in  the  curve ;  want  of  data  is  indicated  by  a 
broken  line. 

2  A  section  of  the  curve  means  the  part  situated  between  two  maxima ;  section 
i  includes  hydrogen  only,  section  2  extends  from  lithium  to  sodium,  &c.     There 
are  probably  several  unknown  elements  with  atomic  weights  greater  than  that  of 
didymium  and  smaller   than  that   of  tantalum ;    the  curve,   if  complete,   would 
probably  be  marked  by  a  sixth  maximum  point  between  caesium  and  thorium, 
this  part  of  the  curve  is  therefore  said  to  comprise  two  sections  (6  and  7). 

15—2 


228  CHEMICAL   STATICS.  [§  IO8 

followed  by  a  group  of  comparatively  negative  elements 
(V,  Cr,  Mn;  Zr,  Nb,  Mo,  Rh,  Ru);  these  again  by  positive 
elements  (Fe,  Ni,  Co,  Cu,  Zn,  Ga;  Pd,  Ag,  Cd,  In);  and  after 
these  comes  a  group  of  negative  and  acid-forming  elements 
situated  on  the  ascending  part  of  the  curve  in  each  section 
(As,  Se,  Br ;  [Sn],  Sb,  Te,  I).  Sections  6  and  7  are  too 
incomplete  to  allow  of  definite  conclusions  being  drawn 
regarding  the  positive  or  negative  character  of  the  elements 
situated  thereon. 

1 08.  Fusibility.  The  melting  points  of  several  elements 
have  been  determined  by  various  observers1;  of  late  especially 
by  Carnelley2,who  has  shewn  that  the  fusibility  of  the  elements 
varies  periodically  with  their  atomic  weights.  The  thin  line3 
curve  on  the  plate  facing  p.  227  graphically  exhibits  this 
connection. 

A  connection  may  be  traced  between  the  positions  of  an 
element  on  the  curve  of  atomic  volumes  and  on  that  of 
fusibility;  as  a  rule,  only  those  elements  which  are  situated 
on  ascending  portions  of  the  former  curve,  are  easily  fusible. 
Generalisations  have  also  been  made  concerning  the  connec- 
tions between  the  atomic  weights  of  groups  of  elements  and 
the  melting  points  of  these  elements  and  some  of  their 
analogous  compounds4.  Thus  the  melting  points  of  the 
haloid  salts  of  the  metals  in  group  II.  (see  table  on  p.  225) 
are  considerably  higher  than  those  of  the  corresponding  salts 
of  the  metals  of  group  III. 

e.g.  MgCl2     MgBr2  ;  CaCl2     CaBr2     CaI2 ;         SrCl2     SrBr2     SrI2  ; 

M.P.  708          695     ;  719         676        631    ;           825        630       507    ; 

but        A12C16      Al2Br6  A12I6. 

M.P.  very  low        90  185. 

1  See  Constants  of  Nature,  Part  I.  and  Supplement  to  do.     Also  L.  Meyer, 
loc.  cit.  pp.  145,  6. 

2  Phil.   Mag.  [5]  8.  315  et  seq.     This   paper  contains  a  good  resume  of  the 
periodic  law. 

3  The  values  of  the  melting  points  used  in  preparing  this  curve  are  taken  for 
the  most  part  from  Carnelley's  paper.     The  data  are  meagre,  hence  many  gaps 
occur  in  the  curve  (indicated  by  the  broken  lines);  many  of  the  numbers,  especially 
those  for  elements  at  and  near  to  maximum  points,  must  be  regarded  as  only 
roughly  approximate  to  the  true  values. 

4  See  Williams  and  Carnelley,  C.  S.  Journal  Trans,  for  1879.  563:  1880.  125. 


§  109]  THE   PERIODIC   LAW.  22Q 

Carnelley1  found  the  melting  point  of  beryllium  chloride  to 
lie  between  585  and  617°,  hence  he  concluded  that  beryl- 
lium belongs  to  group  II.  and  that  the  formula  of  its  chloride 
is  Bed,  (Be  =  9-1),  and  not  BeCl3  or  Be2Cl6(Be  =  I3'i5)2. 
The  data,  so  far  as  obtained,  concerning  the  boiling  points, 
crystalline  forms,  and  expansion  by  heat  of  the  elements, 
indicate  that  the  connection  between  those  constants  and 
the  atomic  weights  of  the  elements  is  of  a  periodic  character3. 

109.  Reasoning  from  certain  assumptions  as  to  the  vi- 
brations of  the  particles  of  solid  elements  at  their  melting 
points,  Pictet4  has  concluded  that  a.  T.J/V  =  constant ;  where 
a  =  coefficient  of  linear  expansion,  T  =  melting  point  in  abso- 
lute temperature,  and  V  =  atomic  volume,  of  any  element. 
This  generalisation  holds  good  for  most  of  the  elements  for 
which  sufficient  data  have  been  obtained  ;  the  value  of  Pictet's 
constant  varies  from  about  3*9  to  about  4'g5. 

Hartley6  has  shewn  that  the  ultra-violet  spectra  of  elements 
of  the  same  series  shew  fairly  marked  analogies  as  regards 
general  character;  the  spectra  hitherto  obtained  do  not  permit 
him  to  affirm,  or  deny,  the  existence  of  numerical  relations 
between  the  different  groups  of  lines,  sufficient  to  establish  a 
definite  periodic  connection  between  the  atomic  weights  of  the 
elements  and  the  wave-lengths  of  the  lines  in  the  elementary 
spectra. 

That  there  exists  a  well-marked  connection,  of  periodic 
character,  between  the  atomic  weights,  and  the  heats  of  com- 
bination of  the  elements  with  chlorine,  bromine  and  iodine 
has  been  shewn  by  A.  P.  Laurie7.  The  data  are  somewhat 

1  Proc.  R.  S.  29.   190.     According  to  more  recent  determinations  by  Nilson 
and  Pettersson  (Ber.  17.  987),  the  melting  point  of  beryllium  chloride  is  joo°  to 


150 


lower  than  the  temperature  given  by  Carnelley. 


See  forward,  par.  in. 

For  details  see  L.  Meyer,  loc.  cit.  pp.  150 — 15*. 
Compt.  rend.  88.  855. 

For  data  see  L.  Meyer,  loc.  cit.  pp.  154—156, 

C.  S.  Journal  Trans,  for  1882.  84  :  permanent  photographs  of  the  ultra-violet 
spectra  of  various  elements  are  given  in  this  paper.    See  also  ibid.  Trans,  for  1883. 

39°- 

7  Phil.   Mag.    (5)    15.    42.      For   data   shewing   that   some   of   the   physical 


230 


CHEMICAL   STATICS. 


[§IIO 


scanty.  The  accompanying  curve  has  been  constructed  from 
the  values  given  by  Thomsen,  in  his  Thennochemischen  Unter- 
suchungen,  for  the  reaction  [M,  Cl],  the  quantities  of  heat  being 
stated  in  kilogram-units. 


100— 

90- 


atomic  weights 


I     \M       I  C/l       I       I       I       P*"  I       ' 
10    Jtso      30     40     50      60      70     80     90     100    no    120    130  140    150    160    170    180    190 


no.  Having  thus  established  the  existence  of  a  connec- 
tion, distinctly  of  a  periodic  character,  between  the  atomic 
weights  and  the  general  nature  of  the  elements,  we  may 
proceed  to  consider  the  more  important  applications  of  the 
periodic  law.  This  consideration  will  also  serve  more  fully 
to  elucidate  the  meaning  of  the  law. 

The  law  has  been  applied  to  predict  the  properties  of 
unknown  elements.  In  the  nomenclature  of  unknown  ele- 
ments Mendelejeff  employs  Sanscrit  prefixes,  eka,  dui,  triy 
&c.  Thus  looking  at  group  IV.  (see  table,  p.  225),  titanium, 
zirconium  and  cerium,  supposing  those  elements  unknown, 
would  be  named  eka-carbon,  dui-carbon  and  tri-carbon.  At 
the  time  of  MendelejefFs  earliest  publication  there  was  no 
element  known  which  could  be  placed  opposite  the  atomic 
weight  69  in  group  III.,  nor  any  which  could  be  placed  oppo- 
site the  atomic  weight  44  in  the  same  group.  The  former  of 
these  hypothetical  elements  Mendelejeff  named  eka-alumi- 

properties  of  compounds,  e.g.  melting  and  boiling  points,  vary  periodically  with 
variations  in  the  atomic  weights  of  the  constituent  elements,  see  Carnelley,  Phil. 
Mag-  [5]  8.  368—  70. 


§110] 


THE   PERIODIC   LAW. 


23l 


nium,  the  latter  he  called  eka-boron.  The  properties  of  eka- 
aluminium  were  predicted  by  Mendelejeff  from  considering 
the  position  of  the  element  in  the  same  group  as,  and  in- 
terposed between,  aluminium  and  indium,  and  in  the  same 
series  as,  and  following  after,  zinc.  In  1875  a  new  metal  was 
discovered  by  L.  de  Boisbaudran.  The  following  table  con- 
tains, in  parallel  columns,  the  leading  properties  of  this  metal, 
and  those  enumerated  by  Mendelejeff  as  characteristic  of 
eka- aluminium',  there  can  be  no  doubt  that  the  hypothetical 
metal  of  Mendelejeff  and  the  gallium  of  de  Boisbaudran  are 
one  and  the  same  element. 


Eka  -alumin  ium. 

Readily  obtained  by  reduction. 

Melting  point  low.     Sp.  gr.  =  5 '9. 

Not  acted  on  by  air. 

Will  decompose  water  at  a  red  heat. 

Slowly  attacked  by  acids  or  alkalis. 

Will  form  a  potassium  alum  more 
soluble,  but  less  easily  crystallis- 
able,  than  the  corresponding 
aluminium  salt. 

Oxide  =  E12O3.     Chloride  =  E12C16. 

Atomic  weight  about  69. 


Gallium. 

Readily  obtained  by  electrolysing 
alkaline  solutions. 

M.p.  =  3o-i5°.     Sp.  gr.  =  5'93. 

Non-volatile,  and  but  superficially 
oxidised  in  air  at  bright  red  heat. 

Decomposes  water  at  high  temper- 
atures. Soluble  in  hot  hydro- 
chloric acid,  scarcely  attacked 
by  cold  nitric  acid ;  soluble  in 
caustic  potash. 

Forms  a  well-defined  alum. 

Chloride  =  Ga2Cl6.     Oxide  =  G  a2O3. 

Atomic  weight  =  697. 

Eka-boron  belongs  to  group  III.;  the  general  formula  for 
the  oxides  of  the  members  of  this  group  is  R2O3 ;  in  its 
properties  eka-boron  ought  to  be  related  to  aluminium  as 
calcium  is  to  magnesium,  and  as  titanium  is  to  silicon.  The 
atomic  weight  of  eka-boron  must  be  about  43 — 46,  inasmuch 
as  it  follows  K  (39)  and  Ca  (40),  and  is  followed  by  Ti  (48) 
and  V  (51).  Reasoning  from  these  data,  Mendelejeff1  pre- 
dicted certain  properties  as  characteristic  of  eka-boron  and  its 
salts.  Some  of  these  are  placed  in  parallel  columns  with  a 
description  of  the  properties  of  the  metal  scandium*,  disco- 
vered in  1879  by  Nilson. 

1  See  translation  of  Mendelejeff  s  paper  in  Chew.  News,  41.  pp.  71 — 72- 

2  Ber.  13.  1439.     See  also  Cleve,  Ber.  12.  2264;  and  Compt.  rend.  89.  419, 
(abstract  of  latter  paper  in  C.  S.  Journal  for  1880.  8,  is  useful). 


232 


CHEMICAL  STATICS. 


[§ 


10 


Eka-boron. 

Atomic  weight  about  44. 

Oxide  Eb2O3  soluble  in  acids ;  sp. 
gr.  about  3*5  ;  analogous  with  but 
more  basic  than  A12O3 ;  less  basic 
than  MgO  ;  insoluble  in  alkalis. 

Salts  of  Eb  colourless,  and  yield 
gelatinous  precipitates  with 
KOH,  K2CO3,  Na2HPO4,  &c. 

Sulphate  Eb2.3SO4  will  form  a 
double  salt  with  K2SO4,  probably 
not  isomorphous  with  the  alums. 

Chloride  EbCl3  or  Eb2Cl6,  sp.  gr. 
about  2,  less  volatile  than  A12C16. 


Scandiu?n. 

Atomic  weight =44. 

Oxide  Sc2O3  ;  sp.  gr.  =  3'8  ;  soluble 
in  strong  acids  ;  analogous  with 
but  more  decidedly  basic  than 
A12O3  ;  insoluble  in  alkalis. 

Solutions  of  Sc  salts  colourless  and 
yield  gelatinous  precipitates  with 
KOH,  K2CO3  and  Na2HPO4. 

Sulphate  Sc2.  3SO4  forms  a  double 
salt,  not  an  alum,  Sc23SO4. 
2K2S04. 


There  is  a  gap  in  group  IV.  series  5.  Eka-silicon  comes 
in  the  group  which  comprises  Si,  Sn,  and  Pb,  and  in  the 
series  including  Ga,  and  As.  This  hypothetical  element  ought 
also  to  shew  analogies  with  other  elements  ;  thus, 

Es  :  Ti  ::  Zn  :  Ca  ::  As  :  V. 

From  the  position  of  eka-silicon1  Mendelejeff  concludes  that 
it  will  be  a  grey  metal,  obtained  by  reducing  the  oxide  by 
sodium,  fusible  with  difficulty ;  it  will  decompose  steam 
very  slowly,  will  be  scarcely  acted  on  by  acids,  but  easily  by 
alkalis.  The  oxide,  EsO2,  (sp.  gr.  about  47)  will  be  obtainable 
by  burning  the  metal  in  air,  it  will  resemble  TiO2,  but  will  be 
less  basic  than  this  oxide,  although  more  basic  than  SiO2 ; 
the  hydroxide  will  be  soluble  in  acids,  but  the  solution  will 
be  easily  decomposed  yielding  an  insoluble  metahydroxide. 
The  oxide  will  yield  a  series  of  double  fluorides  M2EsF6 
(M  =  alkali  metal)  isomorphous  with  the  corresponding  salts 
of  Si,  Ti,  Zn  and  Sn.  The  fluoride  EsF4  will  not  be  gaseous  ; 
the  chloride  EsCl4  will  be  a  volatile  liquid  boiling  at  about 
1 00°.  Eka-silicon  will  form  volatile  organo-compounds.  The 
new  element  will  probably  occur,  along  with  several  other 
unknown  elements,  in  those  complex  minerals  which  contain 
titanium  and  niobium.  It  may  be  separated  from  the  for- 
mer metal  by  taking  advantage  of  the  difference  between 


1  See  Chem.  News,  41.  83. 


§  III]  THE   PERIODIC   LAW.  233 

the  boiling  points  of  the  two  chlorides  (TiCl4,  B.P.=  136°). 
Mendelejeff  thinks  that  the  discrepancies  between  the  num- 
bers obtained  by  Rose,  Pierre  and  others  as  representing  the 
atomic  weight  of  titanium  may  possibly  have  been  due  to  the 
unsuspected  presence  of  EsCl4  in  the  TiCl4  analysed  by  them. 

The  discovery  of  eka-silicon  is  still  in  the  future ;  yet 
looking  to  the  history  of  gallium  and  scandium  we  may 
almost  consider  eka-silicon  as  one  of  the  known  elements. 

in.  The  periodic  law  has  also  been  successfully  used  as 
a  guide  in  the  comparative  study  of  the  properties  of  elements 
already  known. 

To  which  group  of  elements  does  beryllium  belong  ?  Is 
the  formula  of  the  oxide  BeO  or  Be2O3,  and  of  the  chloride 
BeCl2  or  BeCl3  ?  Is  the  atomic  weight  of  beryllium  9  or  13*5  ? 

The  arrangement  of  the  elements  in  accordance  with  the 
periodic  law  seems  to  necessitate  the  placing  of  beryllium  in 
group  II.;  but  recently  amassed  experimental  evidence  sug- 
gests, in  the  opinion  of  some  chemists,  necessitates  in  that 
of  others,  that  this  metal  should  be  placed  in  the  group 
characterised  by  the  power  of  forming  an  oxide  R2O3.  The 
atomic  weight  of  beryllium  =  n  .  9*1.  The  data  regarding  the 
specific  heat  of  beryllium  have  been  presented  in  Chapter  I. 
par.  28,  and  it  has  there  been  shewn  that,  so  far  as  specific 
heat  data  are  concerned,  the  atomic  weight  of  this  element  is 
probably  represented  by  the  number  9*1.  The  specific  heat 
of  beryllium,  we  found,  increases  rapidly  as  temperature  rises, 
and  in  this  respect  shews  an  analogy  with  the  specific  heats 
of  boron,  carbon  and  silicon.  If  the  mean  values  of  the 
specific  heats  for  the  temperature-interval  o°  to  100°  of  the 
metals  in  series  2  and  3  are  multiplied  into  the  atomic 
weights  of  these  metals,  it  is  found  that  the  atomic  heat 
decreases  as  the  fusibilities  of  these  metals  decrease  and  as 
the  atomic  weights  increase  ;  thus, 

Atomic  heat.  Atomic  heat. 

Li,  6-6  Na,  67 

Be,  3-8  [if  Be  =  9-1]  Mg,  5  '9 

B,  2-6  Al,  5'5 

C,  2-4  Si,  4-6 


234  CHEMICAL   STATICS.  [§  1  1 1 

The  value  to  be  assigned  to  the  atomic  weight  of  beryl- 
lium cannot  however  be  regarded  as  finally  settled  by  the 
determinations  already  made  of  the  specific  heat  of  this 
metal. 

Nilson  and  Pettersson1  insist  that  the  molecular  heats  and 
specific  volumes  of  the  oxide  and  sulphate  of  beryllium,  and 
also  the  atomic  heat  of  oxygen  in  this  oxide,  establish  the 
formulae  of  these  bodies  to  be  Be2O3  and  Be2.3SO4  respec- 
tively; and  therefore,  these  chemists  argue  that  the  atomic 
weight  of  the  metal  is  13*65,  and  beryllium  must  be  placed  in 
the  group  which  comprises  aluminium,  gallium,  indium,  &c. 
On  the  other  hand,  Brauner2  gives  data  from  which  it  would 

.          .  ill  A       formula  weightx 

appear    that    the    molecular    volumes    ( i.e. .> —         -<r  ) 

\      specific  gravity/ 

of  beryllium  oxide  and  sulphate,  assuming  the  formulae 
BeO  and  BeSO4  as  correct  (Be  =  9'i),  are  what  might  be 
expected  from  the  position  of  beryllium  (9'i)  in  group  II. 
series  2. 

Brauner3  gives  in  tabular  form  the  data  concerning  the 
molecular  heats  (i.e.  formula  weight  x  specific  heat)  of  metallic 
oxides,  arranging  the  metals  in  groups  and  series.  These 
data  shew  that  the  value  of  the  'molecular  heat'4  of  the 
oxides — calculated  in  each  case  for  one  atom  of  metal  in  the 
oxide — varies  considerably :  '  the  oxides  of  the  metals  of  a 
'  natural  group  have  nearly  the  same  molecular  heats,  but  the 
'  value  increases  as  the  atomic  weights  of  the  metals  increase.' 
If  the  atomic  heat  of  the  metal  in  each  of  these  oxides  is 
deducted  from  the  molecular  heat  of  the  oxide — calculated 
as  mentioned  above — the  remainder  represents  the  '  atomic 
heat  of  oxygen  in  the  oxide/4. 

Brauner  gives  the  following  table. 


1  Ber.  13.  1459.  2  Ber.  14.  53. 

3  Loc.  cit. 

4  These  expressions  must  be  taken  as  meaning,  in  one  case,  the   product 
(formula  weight  x  spec,  heat),  and  in  the  other,  (formula  weight  of  oxide  x  spec, 
heat)  -  (atomic  weight  of  metal  in  oxide  x  spec.  heat). 


§  III]  THE   PERIODIC   LAW.  235 

'  Atomic  heat  of  oxygen  in  metallic  oxides?     (BRAUNER.) 


GROUPS 

I 

II 

III 

IV 

V 

VI 

Series 

2 

Be,  2-4 

B,  2-6 

L 

Mg,  3'8 

Al,  2-6 

Si,  2-8 

4 

Ca,  3-4 

Sc,  27 

Ti,  3'8 

5 

Cu,  4-6 

Zn,  3-9 

Ga,  2-9 

6 

Y,3'5 

Zr,  3-6 

Mo,  4'i 

7 

In,  3-1 

Sn,  3-8 

8 

La,  4-0 

Ce,  4'4 

Di,  4-9 

9 

10 

Yb,  4-2 

W,4-i 

ii 

Hg,  4'8 

12 

Th,  4-0 

The  atomic  heat  of  oxygen  in  the  oxides  increases  as 
the  atomic  weights  of  the  metals  in  each  group  increase ; 
the  value  of  the  atomic  heat  of  oxygen  in  beryllium  oxide  is 
smaller  than  the  value  for  any  other  oxide  in  the  group  ; 
hence  beryllium  should  come  in  group  II,  series  2. 

Carnelley's  determination  of  the  melting-point  of  beryl- 
lium chloride  (see  ante,  par.  108)  points  to  the  beginning  of 
group  II  as  the  proper  position  for  beryllium,  and  hence  to 
the  number  9*1  as  the  atomic  weight  of  this  metal. 

The  general  chemical  characters  of  beryllium  salts  are 
summed  up  in  the  three  statements1  (Be  =  9'i) : 

(1)  Li  :  Be  =Be  :  B 

(2)  Li  :  Na  =  Be  :  Mg=B  :  Al 

(3)  Li  :  Mg=Be  :  Al  =  B  :  Si. 
1  See  Brauner,  Ber.  14.  53. 


236  CHEMICAL   STATICS.  [§  1 1 1 

Hence  we  may  conclude  that  there  is  a  large  probability  in 
favour  of  the  value  9*1  for  the  atomic  weight  of  beryllium. 
This  conclusion  is  supported  by  Hartley's  observations  on  the 
spectrum  of  beryllium  and  his  comparison  of  that  spectrum 
with  those  of  metals  in  group  II.  and  III1. 

Nilson  and  Pettersson  have  very  recently  succeeded  in 
gasifying  beryllium  chloride ;  their  determination  of  the 
density  of  this  compound  in  the  state  of  gas  shews  that  the 
formula  BeCl2  (Be  =  9*1)  really  represents  the  molecular 
weight  of  the  substance2. 

The  mean  values  for  the  atomic  weights  of  the  three 
metals,  cerium,  lanthanum,  and  didymium,  deduced  from  the 
most  trustworthy  data  are 

(i)  (2)  (3) 

If  oxide=MO  :     if  oxide  =  M2O3  :    if  oxide =MO2. 
La=          92-33                         138-5  1847 

Ce=         94  141  188 

Di=         96  144  192 

Numbers  somewhat  smaller  than  the  values  in  column  (i) 
were  formerly  generally  adopted.  In  the  earlier  work  on  these 
metals  very  varying  results  were  obtained  by  different  chemists. 
Mendelejeff  proposed  to  multiply  the  generally  accepted 
atomic  weights  of  cerium  and  didymium  by  1*5  and  that  of 
lanthanum  by  2  ;  he  thus  got  the  values  Ce3=  139;  Di=  138  ; 
La  =  1 80.  If  this  multiplication  is  performed  on  the  more 
accurately  determined  values  given  in  column  (i)  above,  we 
have  Ce=i4i;  Di=i44;  La=i 847. 

Cerium  forms  two  oxides,  CeO  and  Ce3O4  if  Ce  =  94, 
Ce2O3  and  CeO2  if  Ce=i4i.  Mendelejeff  placed  cerium  in 
group  IV,  the  general  formula  for  the  highest  oxide  charac- 
teristic of  this  group  being  RO2 ;  lanthanum  he  placed  in  the 
same  group  but  in  the  series  next  after  that  which  contained 
cerium ;  didymium  found  a  place  in  group  III  (oxide  =  R2O3), 
coming  after  yttrium  and  indium  and  preceding  erbium4. 

1  C.  S.  Journal  Trans,  for  1883.  316.  2  Ber.  17.  987. 

3  In  a  note  (see  Chem.  News,  41.  49,  note)  Mendelejeff  gives  distinct  reasons 
for  thinking  that  this  number,  although  that  deduced  from  the  best  experimental 
evidence  then  available,  is  too  small. 

4  The  atomic  weight  of  erbium  was  not  then  determined  with  any  accuracy. 


§  III]  THE   PERIODIC   LAW.  237 

The  properties  of  cerium  compounds  were  fairly  well 
known  at  this  time,  and  Mendelejeffs  arguments  were  very 
strong1;  the  facts  known  concerning  salts  of  lanthanum  and 
didymium  were  however  scanty,  and  Mendelejeff  did  not 
strongly  press  the  arguments  in  favour  of  the  new  positions 
assigned  them  in  his  scheme  of  classification.  More  recent 
and  trustworthy  work  has  established  the  numbers  in 
column  (i)  above  as  the  equivalents  of  the  three  metals 
(the  atomic  weight  of  erbium  has  also  been  established  as 
about  =  166) ;  hence  the  positions  assigned  by  Mendelejeff  to 
didymium  and  lanthanum  must  be  altered.  Cerium2  remains 
in  group  IV  (RO2),  series  8.  Didymium  occupies  a  posi- 
tion in  series  8  of  group  V ;  the  oxide  Di2O5  and  the  oxy- 
chloride  DiOCl,  which  ought  to  exist  if  this  position  is  cor- 
rect, have  lately  been  obtained  by  Brauner3;  (Di2O5  is  much 
more  stable  than  Bi2O6,  as  would  be  expected  from  the  posi- 
tion of  didymium  in  the  periodic  arrangement).  No  place  is 
however  found  for  La  =1847;  but  if  the  equivalent  of  lan- 
thanum (92-33)  is  multiplied  by  1-5,  then  La  (138-5)  will 
occupy  a  place  also  in  series  8,  but  in  group  III  (R2O3),  being 
preceded  by  indium  and  succeeded  by  an  element,  as  yet 
unknown,  with  atomic  weight  about  160. 

The  numbers  obtained  by  Hillebrand4  for  the  specific 
heats  of  the  three  metals  under  consideration  fully  confirm 
the  values  assigned  to  the  atomic  weights  of  these  metals  by 
the  application  of  the  periodic  law  ;  thus, 

Spec.  heat.  Atomic  heat. 

Ce  0-0448  4*2  if  Ce=  94 

6-3     „     =141 

La  0-0449  4'2  if  La=  92-33 

6-2      „     =138-5 
8-3     „     =1847 

Di  0-0456  4-4  if  Di=  96 

6-6     „     =  144 

1  See  Cheni.  News,  41.  49. 

2  This    position    for    cerium    is    strengthened    by   Brauner's  preparation   of 
CeF4 .  H2O  and  2CeF4 .  ^KF  .  2H2O.     (Brauner,  loc.  cit.) 

3  C.  S.  Journal,  Trans,  for  1882.  73. 

4  PogS'  Ann.  158.  71. 


238  CHEMICAL   STATICS.  [§  1 1  I 

In  the  table  on  p.  225  iodine  and  tellurium  are  placed  in 
series  7,  but  I  >  Te.  The  older  determinations  of  the  atomic 
weights  of  these  elements  made  Te  >  I ;  nor  is  this  result  con- 
tradicted by  the  recent  work  of  Wills1.  Nevertheless  as  the 
numbers  obtained  by  Wills  range  from  126*07  to  128*0,  we 
are,  I  think,  justified  in  provisionally  placing  tellurium  in 
group  VI  and  iodine  in  group  VII.  To  reverse  the  positions  of 
these  elements  would  be  entirely  to  obscure  the  analogies  of 
both  with  other  elements2. 

Uranium  is  another  element  the  comparative  study  of  the 
properties  of  which  has  been  much  advanced  by  the  appli- 
cation of  the  periodic  law.  The  atomic  weight  of  this  element 
has  been  established  as  =  n .  120.  If  n  =  i,  the  three  oxides  of 
uranium  must  be  formulated  UO,  U2O3,  and  U3O4 ;  but  there 
is  no  place  for  an  element  with  this  atomic  weight  and 
forming  these  oxides  in  the  periodic  arrangement.  If  however 
;/  =  2,  then  (11  =  240)  the  oxides  become  UO2,  UO3,  and 
U3O8,  and  uranium  finds  a  place  in  VI — 12.  The  preceding 
members  of  this  group — Cr,  Mo,  W — yield  oxides  (RO3) 
which  are  acid-forming.  But  a  comparative  study  of  the  re- 
lations between  the  properties  of  oxides  and  the  atomic 
weights  of  the  elements  in  these  oxides  shews,  that  as  the 
atomic  weights  of  the  elements  in  a  group  increase,  the  acid 
character  of  the  higher  oxides  formed  by  these  elements  be- 
comes less  marked  (e.g.  CrO3  is  more  markedly  an  acid  oxide 
than  MoO3  or  WO3).  Now  the  highest  oxide  of  uranium  is 
an  acid-forming  oxide,  but  its  acid  functions  are  less  marked 
than  those  of  CrO3,  MoO3,  and  WO3 ;  salts  corresponding  to 
K2CrO4  and  K2Cr2O7  in  which  Cr  is  replaced  by  U  are  known. 
Uranic  chloride,  UC14  if  U  =  240,  resembles  MoCl4  in  being 
volatile  and  decomposable  by  water. 

,  /.       atomic  weight\       r     .       r 

The    atomic    volume      i.e.  -  ~«r~      °f    the    four 

V         spec,  gravity  / 

1  C.  S.  Journal  Trans,  for  1879.  704. 

2  Brauner  has  recently  obtained  values  for  the  atomic  weight  of  tellurium  vary- 
from  124*94  to  125*4  (mean  =  125);   he  has  shewn  that  the  process  employed  by 
Wills  gives  too  high  results  unless  great  precautions  are  taken.     (See  abstract  .in 
Ber.  16.  3055.) 


§112]  THE   PERIODIC   LAW.  239 

metals,  Cr,  Mo,  W,  U,  increases  as  atomic  weight  increases, 
the  values  being  Cr  =  7*6  ;  Mo  =  1 1  ;  W  =  1 1  ;  U  =  12-5. 

Hence  from  the  comparative  study  of  uranium  compounds 
guided  by  the  periodic  law,  we  appear  to  be  justified  in 
adopting  240  as  the  atomic  weight  of  this  metal. 

Recent  determinations  of  the  densities  of  gaseous  uranium 
bromide  and  chloride,  and  of  the  specific  heat  of  pure  ura- 
nium, have  fully  confirmed  this  number  (see  ante>  Chap.  I. 
pars.  19,  and  25). 

112.  The  facts  enumerated  in  the  preceding  pages  un- 
doubtedly establish  the  periodic  law  on  a  firm  basis,  and 
justify  the  employment  of  this  law  as  one  of  the  main  guides 
in  a  general  scheme  of  chemical  classification  *. 

The  following  arrangement  of  the  elements  (the  table  is 
taken,  with  a  few  alterations,  from  a  paper  by  Mendelejeff  in 
Ber.  13.  1804)  is  in  the  opinion  of  Mendelejeff  himself  the 
best  for  clearly  setting  forth  the  general  teaching  of  the 
periodic  law.  (See  next  page.) 

Each  group — except  group  VIII — contains  members  be- 
longing to  odd  and  to  even  series;  or  it  may  be  said  that 
each  vertical  column,  or  large  series,  is  subdivided  into  two 
parts  having  seven  elements  in  each.  The  entire  column, 
comprising  an  odd  and  an  even  series,  forms  a  '  long  period ' ; 
the  seven  members  in  the  even  or  in  the  odd  series  form 
a  'short  period.'  The  members  of  group  VIII  form  'transition 
'periods'  from  series  4  to  5,  6  to  7  (probably  8  to  9),  and 
10  to  ii.  Including  the  'transition  periods,'  each  'long 
period'  theoretically  contains  17  elements. 

Because  of  its  peculiar  properties,  and  also  because  of  the 
anomalous  relations  between  the  values  of  its  atomic  weight 
and  those  of  succeeding  elements,  hydrogen  is  regarded  as 
the  sole  representative  of  group  I,  series  I. 

Comparing  series,  we  find  closer  analogies  between  corre- 
sponding members  of  odd  or  of  even  series,  than  between 
those  of  odd  and  even  series  :  thus,  comparing  series  4  and  6, 

1  It  is  very  unfortunate  that  MendelejefFs  Treatise  on  Chemistry,  in  which,  as 
I  understand,  this  law  is  made  the  basis  of  a  general  system,  should  not  be 
published  in  some  one  of  the  languages  of  Western  Europe. 


240 


CHEMICAL  STATICS. 


[§II2 


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§112]  THE   PERIODIC   LAW.  24! 

and  4  and  7,  potassium  and  rubidium  are  seen  to  be  more 
closely  related  than  potassium  and  silver ;  calcium  and  stron- 
tium, than  calcium  and  cadmium;  vanadium  and  niobium,  than 
vanadium  and  antimony.  Again,  comparing  series  5  and  7, 
and  also  5  and  6,  it  is  seen  that  the  relations  between  zinc 
and  cadmium,  or  between  arsenic  and  antimony,  are  closer 
than  those  between  zinc  and  strontium,  or  arsenic  and  nio- 
bium. 

Omitting  the  typical  elements,  it  may  be  said  that,  as  a 
rule,  the  most  markedly  nonmetallic  elements  are  placed  in 
odd  series.  Also,  that  the  passage  from  an  even  to  an  odd 
series  is  accompanied  by  a  gradual  change,  but  that  from  an 
odd  to  an  even  series  by  a  more  sudden  change  in  the  pro- 
perties of  the  elements ;  thus  chromium  and  manganese 
resemble  copper  and  zinc  much  more  than  selenion  and 
bromine  resemble  rubidium  and  strontium,  or  than  tellurium 
and  iodine  resemble  caesium  and  barium.  It  may  also  be 
laid  down  as  a  general  proposition  that  volatile  organo- 
metallic  compounds  are  formed  only  by  metals  which  occur 
in  odd  series ;  should  such  compounds  be  hereafter  formed 
containing  metals  which  belong  to  even  series,  the  properties 
of  the  compounds  in  question  will  probably  differ  much  from 
those  of  the  volatile  organo-metallic  compounds  at  present 
known.  (Mendelejeff.) 

The  elements  which  form  the  '  transition  periods '  (group 
Vlll)  possess  many  characteristic  properties.  They  are  very 
infusible,  have  small  atomic  volumes,  and  occlude  oxygen 
and  other  gases ;  oxides  of  the  form  RO4  are  met  with  in  this 
group  only;  the  highest  oxides  are  basic  or  very  feebly 
acid ;  these  metals  form  stable  alkaline  double  cyanides 
K4RCy6,  K3RCy6,  or  K2RCy4,  and  also  stable  ammoniacal 
compounds1. 

The  elements  in  series  2  (from  lithium  to  fluorine),  and 
perhaps  the  first  member  of  series  3,  viz.  sodium,  are  grouped 
together  as  'typical'  elements.  There  is  no  'transition 
'  period '  coming  between  the  even  series  2  and  the  odd 

1  See  Mendelejeff,  Chcm.  A'civs,  40.  267. 
M.  C.  1 6 


242  CHEMICAL  STATICS.  [§  H3 

series  3  as  there  is  between  series  4  and  5,  6  and  7,  and  10 
and  ii.  The  mean  difference  between  the  atomic  weights  of 
two  elements  in  successive  even  series  and  in  the  same  group 
(e.g.  between  potassium  and  rubidium,  or  between  rubidium 
and  caesium)  is  45  ;  but  the  mean  difference  between  the 
atomic  weight  of  an  element  in  series  4  and  the  corre- 
sponding element  (i.e.  the  element  in  the  same  group)  in 
series  2  is  35  :  hence  we  should  expect  to  find  the  relations 
of  series  2  to  other  series  different  from  the  general  mutual 
relations  exhibited  by  these  other  series.  As  the  lower  mem- 
bers of  an  homologous  series  of  carbon  compounds  are  some- 
times characterised  by  the  possession  of  properties  which  do 
not  belong  to  the  higher  members,  so  the  elements  with 
atomic  weights  ranging  from  I  to  19  (?23)  are  characterised 
by  special  properties;  they  are  'typical'  elements. 

113.  As  the  atomic  weight  increases  in  each  group,  the 
basic  character  of  the  higher  oxides  formed  by  the  members 
of  the  group  becomes  more  marked,  and  at  the  same  time 
these  oxides  become  more  easily  reduced.  It  is  also  to  be 
noted  that  the  composition  of  the  more  stable  haloid  and 
oxyhaloid  salts  (and  in  some  cases  of  the  more  stable  salts  as 
a  whole)  tends,  as  atomic  weight  increases,  to  correspond  in 
form  with  an  oxide  containing  less  oxygen  than  the  highest 
oxide.  These  statements  hold  good  more  especially  for  those 
members  of  a  group  which  occupy  the  odd  series.  Group  V 
presents  a  good  example.  Sb2O5  is  more  basic  than  P2O5,  and 
Bi2O5  is  marked  by  an  almost  complete  absence  of  acid  pro- 
perties. The  highest  oxides  of  this  group  belong  to  the  form 
RX5  (see  p.  243) ;  the  stable  haloid  and  oxyhaloid  salts  of 
phosphorus,  vanadium,  niobium  (PF5,  VOC13,  NbCl5),  belong 
to  the  same  form,  but  the  bismuth  haloid  and  oxyhaloid  salts 
are  Bid,,  BiBr3,  BiOCl,  BiOBr,  &c.,  which  belong  to  the 
form  RX^  characteristic  of  the  lower  oxide  Bi2O3. 

The  first  and  last  members  of  a  series,  and  more  especially 
of  a  '  long  period,'  present  marked  differences  in  their  general 
chemical  behaviour;  thus  lithium,  potassium,  and  rubidium, 
the  first  members  of  the  long  periods  I,  2,  and  3,  are  strongly 
positive,  whereas  the  last  members  of  the  same  periods, 


§  114]  THE  PERIODIC  LAW.  243 

viz.  chlorine,  bromine,  and  iodine,  are  typically  negative 
elements. 

114.  The  form  of  the  highest  oxides,  and  of  some  of  the 
other  salts,  appears  to  be  a  periodic  function  of  the  atomic 
weights  of  the  elements.  In  dealing  with  this  question  it  will 
be  well  to  use  the  term  '  formula  weight  '  rather  than  mole- 
cular weight,  as  the  molecular  weights  of  very  few  oxides 
have  been  determined. 

If  R  be  used  to  represent  the  amount  of  an  element  ex- 
pressed by  its  atomic  weight,  and  X  to  represent  the  amounts 
of  Cl,  Br,  I,  F,  expressed  by  the  respective  atomic  weights  of 
these  elements,  or  the  amounts  of  the  groups  (OH),  (NO3), 
(C1O3),  &c.,  expressed  by  these  formulae,  or  the  amounts  of 
the  following  elements  or  groups  of  elements  expressed  by 
half  the  formulas,  viz.  O,  S,  (SO4),  (CrO4),  &c.,  then  we  may 
say  that  the  oxides 

R20,  RO,  R203,  ROZ,  Rz05t 
belong  respectively  to  the  forms 

RX,  RX  2,  RX^  RX  4, 
also  that  the  salts 


8;  ROC\3 
belong  respectively  to  the  forms 

RX-,  RXj  RX3,  RX3,  RX3,  RXS;  RXb. 

It  becomes  possible  to  give  general  expressions  for  the 
forms  of  the  highest  stable  oxides  characteristic  of  each 
group  ;  thus, 

Group    i  ii  in          iv  v  vi  vn  vin 

R20 
or        RX 

This  statement  may  be  put  thus  ;  the  number  of  oxygen 
atoms  in  the  general  expression  for  the  highest  stable  oxide 
characteristic  of  each  member  of  a  series  increases,  as  the 
atomic  weights  of  the  members  of  the  series  increase. 

Most  of  the  stable  salts  (haloid  salts,  oxyhaloid  salts, 
nitrates,  sulphates,  chromates,  phosphates,  £c.)  characteristic 

1  6—  2 


244  CHEMICAL   STATICS.  [§  114 

of  the  members  of  each  group  belong  to  the  same  general  form 
(RX,  RXZ,  &c.)  as  the  oxides.  But  in  every  group  well- 
marked  salts  are  known  which  belong  to  higher  forms  than 
the  oxide  form :  thus,  some  of  the  members  of  group  I  form 
peroxides  (K2O2,  K2O4,  &c.) ;  some  of  the  elements  in  group 
II  form  salts  (such  as  K2BeF4,  K2ZnCl4,  &c.)  of  the  form 
RX6\  salts,  such  as  BOC13,  KBF4,  KAlBr4,  &c.,  belonging 
to  the  form  RX6,  are  found  in  group  III.  The  forms  of  the 
highest  salts  belonging  to  each  group,  and  also  the  oxide 
forms,  are  given  by  Brauner1;  thus, — 


Groups,  i  ii         in         iv          v          vi          vn         vm 

Salt  forms,      RX7     RX6     RX,     RX±      RX3      RX2      RX      (R2X\ 
Oxide  forms,   R2O      R2O2    R2O3    ^2O4     R2O$     R2O6    (7?2O7)    \R2oJ 

or  thus — 

Salt  forms,      RX,     RX6     RX&     RX±      RXS      RX2      RX      (R2X\ 
Oxide  forms,  RX      RX2     RX3     RX±      RX5      RXS     (RXJ    \RXj 

The  statements  generalised  in  these  expressions  can  be 
accepted  only  as  rough  approximations  to  general  truths. 
Oxides  of  the  forms  given  in  the  table  are  sometimes  less 
stable  than  oxides  of  other  forms — e.g.  CuO  is  more  stable 
than  Cu2O,  PbO  than  PbO2,  &c. ;  the  form  chosen  for  the 
highest  oxides  is  sometimes  scarcely  known  to  be  represented 
by  actually  occurring  compounds, — thus  the  form  ^2O7,  cha- 
racteristic of  group  VII,  finds  its  only  representative  in  I2O7 , 
and  the  existence  of  this  oxide  cannot  be  regarded  as  proved. 
Again,  salts  belonging  to  the  general  expressions  given  as 
representing  the  highest  forms  are  sometimes  fairly  character- 
istic of  the  group,  in  other  cases  it  is  only  by  a  dexterous 
manipulation  of  formulae  that  the  existence  of  such  salts  can 
be  discovered  ;  thus  a  great  many  well-marked  salts  of  the 
members  of  group  V  undoubtedly  belong  to  the  form  RXZ, 
but  it  is  only  by  having  recourse  to  such  a  substance  as 
NaOH.3H2O  that  a  salt  of  the  form  RX7  can  be  found 
belonging  to  group  I. 

1  Sitzberichte  der  K.  Akad.  zu  Wien,  (tnath-natnriviss.  classe)  84.  1165. 


§  115]  THE   PERIODIC   LAW.  245 

Relations  can  be  traced  between  the  general  forms  of 
hydrogen  and  hydroxyl  compounds,  especially  in  groups  IV, 
V,  VI,  and  VII ;  thus, — 

Group,        iv  v  vi  vn 

Hydrogen  compounds,      7?H4  7?H3  /?H2  ^H 

e.g.      SiH4  PH3  SH2  C1H 

Hydroxyl  compounds,      ^?H4O4        /?H3O4        7?H2O4         7?HO4 

e.g.     Si(OH)4      PO(OH)3    SO2(OH)2   C1O3(OH) 

Dalton,  and  after  him  Berzelius,  sought  to  elucidate  the 
laws  of  atomic  synthesis  ;  they  strove  to  find  forms  capable 
of  expressing  the  maximum  number  of  atoms  of  this  or  that 
element  which  could  combine  to  form  salts.  But  much  had 
to  be  done  before  these  limiting  forms  could  be  found :  a  firm 
standing  ground  appears  to  be  now  gained  in  the  periodic 
law;  to  build  a  structure  worthy  of  the  foundation  must  be 
the  work  of  the  future. 

115.  The  valency  of  the  elementary  atoms  probably 
varies  periodically  with  the  relative  weights  of  these  atoms. 
Thus  taking  series  2,  and  assuming  that  the  atom  of  lithium 
is  monovalent  and  that  of  beryllium  divalent,  it  is  seen  that 
in  this  series  the  valency  of  the  elementary  atoms  increases 
from  one  to  four,  and  again  diminishes  from  four  to  one ; 

Li          Be          B          C          N          O          F 
Valency,     i  234321. 

If  the  evidence  were  sufficient  to  warrant  the  assumption 
that  the  valency  varies  in  every  series  in  the  same  way  as  in 
series  2,  we  should  have  in  the  periodic  law  a  most  important 
aid  towards  determining  the  valencies  of  all  the  elementary 
atoms.  But  the  evidence  at  present  available  concerning 
valency  does  not  permit  us  to  make  this  assumption.  A  pro- 
bable value  for  the  valency  of  an  elementary  atom  may  be 
deduced  from  the  position  of  the  element  in  the  periodic 
arrangement,  but  this  value  must  not  be  considered  as  final. 
It  has  indeed  been  sought  to  fix  the  valencies  of  elementary 
atoms  from  considerations  drawn  from  the  positions  of  these 
elements  in  the  periodic  classification;  but  this  has  been 
done  only  by  attaching  to  the  term  'valency'  a  much  looser 


246  CHEMICAL  STATICS.  [§  1 1 5 

meaning  than  that  which  I  have  attempted  to  shew  must  be 
given  if  an  exact  theory  is  to  be  developed.  In  applying 
the  periodic  law  to  determine  the  valencies  of  elementary 
atoms,  the  formulae  of  oxides  and  of  solid  salts  gene- 
rally have  been  employed  as  data  from  which  conclusions 
might  be  drawn.  But  if  we  define  the  valency  of  an 
atom  as  the  maximum  number  of  other  atoms  with  which 
the  given  atom  can  combine  to  form  a  molecule,  then,  to 
deduce  valencies  from  a  study  of  solid  salts  we  must  assume, 
(i)  that  the  formula  of  a  solid  salt  certainly  represents  at 
least  the  proportion  between  the  numbers  of  atoms  of  each 
element  in  the  molecule;  (2)  that  the  atom,  the  valency  of 
which  is  to  be  determined,  acts  on,  and  is  acted  on  by,  certain 
other  atoms  in  the  molecule — in  some  cases  it  may  be  action 
is  assumed  between  all  the  atoms,  in  other  cases  only  between 
some  of  the  atoms,  in  the  molecule;  and  (3)  we  must  assume 
a  value  for  the  valency  of  each  atom,  other  than  the  given 
atom,  in  the  molecule.  Thus,  to  take  an  extreme  case 
hydrated  chloroplatinic  acid,  H2PtCla .  6H2O,  has  been 
represented  thus — 

VIII        III       IV 

H2Pt(-Cl  =  0  =  H2)6 

in  order  that  the  platinum  atom  may  be  represented  as  octo- 
valent. 

I  have  already1  discussed  assumptions  (2)  and  (3),  and 
have,  I  hope,  shewn  how  vague  and  unsatisfactory  any  theory 
of  valency  must  be  which  in  the  present  state  of  knowledge  is 
based  on  the  study  of  other  than  gaseous  compounds.  A  solid 
compound  is  prepared  with  definite  properties;  analysis  serves 
to  fix  the  composition;  the  atomic  weights  of  the  elements  in 
the  compound  being  known,  a  formula  is  found: — but  to 
assume  that  this  formula  necessarily  represents  the  ratio 
between  the  numbers  of  different  elementary  atoms  in  the 
molecule  of  this  compound,  is  I  think  more  than  a  fair  inference 
from  the  facts.  For  is  not  this  to  assume  that  the  'chemical 
unit'  of  the  solid  compound  is  a  molecule,  whereas  it  may 

1  See  chapter  11.  section  3,  par.  63. 


§  115]  THE   PERIODIC   LAW.  247 

very  possibly  be  a  group  of  molecules?  The  definition  of 
'molecule'  is  a  physical  definition,  and  is  strictly  applicable 
only  to  gaseous  bodies.  The  properties  of  a  solid  may  be 
the  properties  of  a  number  of  little  definite  parts,  each  of 
which  decomposes  into  two  or  more  simpler  groups  (molecules) 
when  the  solid  is  gasified ;  the  ratio  between  the  numbers  of 
atoms  in  the  true  molecules  may  be  different  from  the  ratio 
between  the  numbers  of  atoms  in  those  groups  of  molecules, 
which  form  the  building-stones  of  the  solid  compound. 

But  it  may  be  urged  that  a  much  wider  meaning 
ought  to  be  given  to  the  term  valency.  Better,  I  would 
reply,  employ  another  term,  or  terms.  Let  us  build  as  far 
as  we  can  on  the  theory  of  valency;  so  far  as  it  goes  it  is 
definite,  without  it  the  chemistry  of  carbon  compounds 
especially  could  not  have  made  the  advances  which  it  has 
made.  But  it  is  not  all.  The  periodic  law  emphasises  the 
existence  of  typical  forms  for  the  compounds  of  elements; 
it  points  to  limiting  values  for  the  numbers  of  atoms  which 
can  be  associated  together  in  groups.  It  teaches  the  im- 
portance, in  the  chemistry  of  solid  and  liquid  compounds,  of 
the  law  of  multiple  proportions.  It  reminds  us  that  at  present 
we  must  study  the  properties  of  groups  of  compounds,  that  we 
must  sum  up  these  properties  in  the  simplest  possible  formulae, 
and  that  the  whole  chemical  history  of  each  compound  must 
determine  the  form  to  be  given  to  the  symbol  by  which  we 
express  that  history.  It  tells  us  that,  although  we  do  not 
know  whether  such  formulae  do  or  do  not  represent  the 
relative  weights  of  the  molecules  of  the  bodies  formulated, 
nevertheless  these  formulae  can  be  classified  under  a  few 
types;  and  that  thus  a  certain  amount  of  order  can  be  intro- 
duced into  the  classification  of  solid  and  liquid  compounds, 
general  conclusions  can  be  drawn,  and  predictions  can  be 
made  which  may  be  submitted  to  the  test  of  experiment. 
And  while  doing  this,  the  periodic  law  keeps  before  us  the 
necessity  of  from  time  to  time  modifying  our  scheme  of 
classification ;  it  reminds  us  that  a  typical  classification  is  of 
necessity  temporary,  but  that  just  by  reason  of  its  elasticity  it 


248  CHEMICAL  STATICS.  [§  I  I  5 

is  suited  to  the  present  needs  of  the  chemistry  of  solid  and 
liquid  substances1. 

1  It  is  interesting  to  observe  in  the  applications  of  the  periodic  law  the  survival, 
in  modified  and  more  precise  form,  of  the  old  conception  of  the  element  as  an 
essence  or  principle,  capable  of  impressing  on  all  substances  into  which  it  entered 
properties  sufficiently  definite  to  mark  off  these  substances  from  all  others  which 
did  not  contain  this  principle. 

An  interesting  and  important  paper  on  the  periodic  law,  especially  as  applied 
to  the  classification  of  elements  and  compounds,  by  T.  Bayley,  will  be  found  in 
Phil.  Mag.  (5)  13.  26. 

An  important  paper  has  just  appeared  by  Carnelley  (Phil.  Mag.  for  July,  1884), 
in  which  the  periodic  law  is  illustrated  by  considering  the  melting  and  boiling 
points,  and  to  some  extent  also  the  heats  of  formation,  of  the  halogen  compounds 
of  the  elements ;  and  the  facts  thus  obtained  are  applied  to  determine  the  values 
to  be  assigned  to  the  atomic  weights  of  various  elements,  and  also  the  positions  of 
these  elements  in  the  general  scheme  of  classification  based  on  the  law  in  question. 
The  case  of  beryllium  is  considered  in  detail  in  this  paper. 


§ii6] 


CHAPTER  IV. 

APPLICATION    OF    PHYSICAL     METHODS    TO    QUESTIONS    OF 
CHEMICAL    STATICS. 

116.  CHEMISTRY  being  a  more  concrete  science  than 
physics  must  of  necessity  derive  help  in  solving  its  problems 
from  the  use  of  physical  methods  of  investigation :  but  while 
using  such  methods  the  chemist  ought  not  to  forget  that  his 
aim  is  to  find  answers  to  chemical,  not  to  physical  questions. 

Minute  descriptions  of  physical  processes,  and  details  of 
physical  experiments  are  not  demanded  in  a  treatise  on 
physical  chemistry;  much  less  is  there  required  elaborate 
enunciations  of  the  methods  of  calculation  employed  in 
physical  researches.  Such  things  give  it  is  true  an  appearance 
of  great  accuracy  and  profound  knowledge;  but  the  ap- 
parently accurate  knowledge  and  full  discussion  of  physical 
details  too  frequently  serves  as  an  excuse  for  loose  state- 
ments and  superficial  generalisations  regarding  those  vital 
chemical  questions  for  answering  which  so  vast  a  collection  of 
'  precautionary  and  vehiculatory  gear '  has  been  provided.  In 
attempting  to  give  an  outline  of  the  more  important  appli- 
cations of  physical  methods  to  chemistry  one  is  also  liable  to 
err  in  the  other  direction  :  vague  statements  to  the  effect  that 
the  boiling  points  of  homologous  hydrocarbons  exhibit  constant 
differences,  or  that  the  molecular  structure  of  carbon  com- 
pounds is  intimately  connected  with  their  optical  activity,  or 
that  chemical  actions  which  involve  a  loss  of  energy  in  the 
reacting  systems  frequently  occur, — statements  such  as  these 
are  utterly  inadequate. 


250  CHEMICAL  STATICS.  [§  1 17 

I  cannot  hope  to  avoid  both  dangers :  but  I  may  venture 
to  believe  that  the  contents  of  the  present  chapter  will  be  of 
some  assistance  to  those  who  attempt  to  gain  clear  con- 
ceptions on  the  important  phenomena  forming  the  subject- 
matter  of  physical  chemistry. 

Of  the  physical  methods  employed  by  the  chemist  as  aids 
in  attempts  to  solve  the  questions  of  chemical  statics,  I  shall 
consider  (i)  thermal  methods,  (2)  optical  methods,  (3)  methods 
which  involve  measurements  of  the  volumes  of  reacting  sub- 
stances, and  (4)  methods  based  on  determinations  of  '  etheri- 
fication-values '. 


SECTION  I.     Thermal  Methods*. 

117.  The  principle  of  the  conservation  of  energy  lies  at 
the  root  of  all  thermo-chemical  investigation.  When  two  or 
more  chemical  substances  react  so  as  to  produce  a  new 
system,  or  new  systems  of  substances,  mechanical  work  may 
be  done  by  expansion,  electrical  currents  may  be  produced, 
heat  may  be  generated,  and  energy  may  be  lost  in  the  forms 
of  sound  or  radiant  heat.  The  sum  of  these  various  kinds  of 
energy,  together  with  the  energy  remaining  in  the  final  system, 
must  be  equal  to  the  energy  which  was  present  in  the  original 
system.  A  very  large  part  of  the  energy  lost  during  chemical 
changes  generally  leaves  the  changing  systems  in  the  form  of 
heat ;  hence,  measurements  of  the  quantities  of  heat  evolved 
during  definite  chemical  processes  afford  valuable  information 
with  respect  to  the  differences  between  the  amounts  of  energy 
possessed  by  the  systems  in  their  original  and  final  states. 
To  measure  such  differences  of  energy  is  the  primary  aim  of 
thermal  chemistry. 

1  Principal  text-books  on  the  subject  are  NAU MANN'S  Lehr-  tind  Handbuch 
der  Thermochemie  (1882).  THOMSEN'S  Thermochemische  Untersuchungen,  con- 
taining in  a  systematic  form  the  work  of  many  years  which  has  hitherto  been 
scattered  through  various  memoirs:  3  vols.  are  now  (1884)  published.  BERTHE- 
LOT'S  Essai  de  Mecanique  Chimique  fondee  sur  la  Thermochimie,  2  vols.  (1879) 
with  supplement.  JAHN'S  Die  Grundscitze  der  Thermochemie  (1882). 


§§117,  118]      APPLICATION   OF   PHYSICAL  METHODS.  251 

We  are  accustomed  to  conceive  of  most  chemical  changes 
as  divisible  broadly  into  two  parts,  (i)  separation  of  molecules 
into  atoms,  (2)  re-arrangement  of  atoms  to  form  new  mole- 
cules. We  picture  to  ourselves  the  final  arrangement  of  the 
atoms  as  dependent  on  the  nature  of  these  atoms,  and  on  their 
relative  positions  in  the  molecules  which  composed  the  original 
system,  that  is  to  say,  we  picture  the  progress  of  mutual 
actions  and  reactions  among  the  separated  atoms.  As  we 
know  little,  or  nothing,  of  the  causes  of  this  re-arrangement, 
we  are  accustomed  to  say  that  'the  atoms  are  attracted  towards 
each  other  by  the  force  of  chemical  affinity '. 

Consideration  of  the  circumstances  under  which  chemical 
changes  proceed  will,  I  think,  make  it  evident  that  measure- 
ments of  the  quantities  of  heat  evolved  during  these  changes 
do  not  represent  measurements  of  the  'chemical  affinities'1  of 
the  reacting  atoms ;  but  these  measurements  do  enable  us  to 
draw  conclusions  as  to  the  constitution  of  chemical  sub- 
stances, and  the  general  laws  of  chemical  change. 

The  bearing  of  thermochemical  measurements  on  the 
subject  of  affinity  and  chemical  equilibrium  in  general  will  be 
considered  in  the  second  book :  in  the  present  section  I  pro- 
pose to  give  a  sketch  of  the  methods  of  thermal  chemistry, 
and  a  summary  of  the  more  important  results  obtained  re- 
lating to  allotropy,  isomerism,  nascent  state,  and  other  phe- 
nomena of  chemical  statics. 

1 1 8.  The  notation  of  thermal  chemistry  is  very  simple: 
the  formulae  of  the  reacting  substances  are  enclosed  in  a 
square  bracket,  and  each  formula  is  separated  from  the  other 
by  a  comma.  Thomsen  writes  the  figure  expressing  the 
number  of  atoms  of  each  element  above  the  symbol  of  that 
element. 

Thus,  the  formula  [H2,  Cl2]  =  44,000  +,  means  that  a 
quantity  of  heat  sufficient  to  raise  the  temperature  of  44,000 
grams  of  water  from  o°  to  i°  C,  is  evolved  during  the  chemical 
process  represented  in  ordinary  notation  by  H2  +  C12  =  2HC1, 
the  quantities  of  hydrogen  and  chlorine  being  taken  in  grams2. 

1  Seeflost,  book  n.  chap.  in. 

2  The  unit  of  heat  employed  in  this  section  is  always  to  be  taken  as  the  gram -unit. 


252  CHEMICAL   STATICS.  [§  IlS 

The  symbol  Aq,  separated  by  a  comma  from  another  symbol, 
means  that  a  large  excess  of  water  is  present  and  that  its 
effect  in  the  total  thermal  change  is  taken  into  account ; 
thus,  [HC1,  Aq]  =  17,320+,  means  that  in  the  absorption  of 
36*5  grams  of  hydrochloric  acid  by  an  unlimited  amount  of 
water,  17,320  gram-units  of  heat  are  evolved  ;  [H2,  Cl2,  Aq] 
=  61,320  +,  means  that  the  combination  of  2  grams  of 
hydrogen  with  71  grams  of  chlorine  in  the  presence  of  an 
unlimited  amount  of  water  is  attended  with  the  evolution  of 
61,320  gram-units  of  heat.  [HClAq,  KOHAq]  =  13,750 +  , 
means  that  when  36^5  grams  of  HC1  dissolved  in  a  large 
excess  of  water  react  on  56  grams  of  KOH,  also  dissolved  in 
a  large  excess  of  water,  13,750  gram-units  of  heat  are  evolved. 
The  symbol  H2O  is  used  as  in  ordinary  notation  to  repre- 
sent 1 8  grams  of  water;  thus 

(1)  [Mn,  O2,  SO2,  4H20]  =  190,810+; 

(2)  [MnS044H20,  Aq]=      1770+; 

mean,  (i)  that  In  the  formation  of  the  amount,  in  grams, 
of  crystallised  manganous  sulphate  expressed  by  the  formula 
MnSO44H2O,  from  the  amounts,  in  grams,  of  manganese, 
oxygen,  sulphur  dioxide,  and  water,  expressed  by  the  respec- 
tive formulae  Mn,  O2,  SO2,  and  4H2O,  190,810  gram-units 
of  heat  are  evolved  :  (2)  that  in  the  solution  of  the  foregoing 
number  of  grams  of  crystallised  manganous  sulphate  in  an 
unlimited  quantity  of  water  1770  gram-units  of  heat  are 
evolved. 

An  ordinary  chemical  equation  may  be  supplemented  by 
the  corresponding  thermal  symbol.     Thus 

H2  +  C12=2HC1  +  [H2,  Cl2]  ; 

i.e.  2  grams  of  hydrogen  combine  with  71  grams  of  chlorine 
to  give  73  grams  of  hydrochloric  acid,  and  the  change  is 
attended  with  the  evolution  of  a  definite  amount  of  heat. 
The  fact  that  the  decomposition  of  2HC1  into  H2  and  C12  is 
attended  with  the  absorption  of  the  same  quantity  of  heat  as 
is  evolved  during  the  union  of  H2  with  C12  may  be  expressed 

thus 

2HC1=H2  +  C1-[H2,  Cl2]1. 

1  This  notation  is  however  confused  and  awkward,  and  is  scarcely  used. 


§  I  1  8]  APPLICATION    OF   PHYSICAL   METHODS.  253 

Generally  then1,  let  r  =  the  thermal  value  of  a  chemical 
change  :  let  the  change  be  the  formation  of  a  definite  amount 
of  a  compound2  (viz.  XaYbZ^,  consisting  of  a  parts  by 
weight  of  the  element  X,  b  parts  by  weight  of  the  element  Yy 
and  c  parts  by  weight  of  the  element  Z  ';  then 

r=[X*,  Y\  Z<\  ...........................  (i). 

Let  the  compound  Xa  YbZc  be  produced  as  before,  but  in 
presence  of  a  large  excess  of  water  which  holds  it  in  solution, 
then 

r=[A-«,   K*,  ZS  Aq]   ........................  (2). 

Let  the  substance  Xa  YbZc  already  existing  be  dissolved  in 
an  unlimited  amount  of  water,  then 

r=[A-«y*Z',  Aq]  ...........................  (3). 

Let  the  compound  JTFbe  decomposed  by  the  element  Z 
with  formation  of  XZ  and  Y,  we  get  the  expression 

]  =  [X,Z]-[X,  F]  ..................  (4), 


that  is,  the  total  thermal  change  consists  of  two  parts,  (a) 
the  heat  absorbed  in  separating  XY  into  X  +  Y,  and  (b) 
the  heat  evolved  in  the  union  of  X  and  Z  to  form  XZ. 

Finally  let  the  compound  XY  react  on  the  compound 
ZV  to  produce  XZ  and  FF,  the  value  of  r  is  found  by 
the  formula 

]-[X,  Y]-[Z,  V\  ...............  (5). 


Equations  (i)  to  (3)  have  been  already  illustrated.  As  an 
example  of  the  use  of  (4)  we  may  take  the  action  of  zinc  on 
hydrochloric  acid  whereby  zinc  chloride  and  hydrogen  are 
produced  ; 

[Zn,  2HCl]  =  [Zn,  C12]-2[H,  Cl]  ; 

or  that  of  iron  on  a  solution  of  copper  sulphate  to  produce 
ferrous  sulphate  and  copper  ; 

[CuSO4Aq,  Fe]=[Fe,  SO4Aq]-[Cu,  SO4Aq]. 

1  Thomsen,  Thermochemische  Untersnc/nmgen,  1.  5  ct  seq. 

2  In  many  cases  we  may  use  the  term  '  molecule'  in  place  of  'definite  amount', 
and  'atom'  in  place  of  'parts  by  weight':  but  as  we  shall  frequently  deal  with 
solids  and  liquids  it  is  better  at  present  not  to  speak  of  atoms  and  molecules. 


254  CHEMICAL   STATICS.  [§JI9 

As  an  illustration  of  (5)  the  decomposition  of  PbO  by  H2S 
resulting  in  production  of  PbS  and  H2O,  may  be  used  ; 

[PbO,  H»S]=[Pb,  S]  +  [H2,  0]-[Pb,  0]-[H2,  S]1. 

119.  A  distinction  is  generally  drawn  between  so-called 
exothermic  and  endothermic  changes;  the  former  are  ac- 
companied by  evolution,  the  latter  by  absorption  of  heat. 

Let  (PaQb)  represent  the  energy  in  a  compound  formed  of 
a  parts  of  element  P  and  b  parts  of  element  Q  :  let  (Pa)  and 
(Qa)  represent  the  energy  in  a  parts  of  P,  and  in  b  parts  of 
Q  respectively  ;  then,  inasmuch  as  the  energy  in  any  system 
resulting  from  a  definite  chemical  change  is  equal  to  the 
difference  between  the  energy  in  the  original  system  from 
which  it  was  produced  and  that  lost  during  the  process,  it 
follows  that 


assuming  that   the  heat  evolved  in  the  formation  of  PaQb 
measures  the  total  loss  of  energy. 

And  .-.  (Pa}  +  (Qb}>(PaQb}. 

This  equation  represents  an  exothermic  change. 

But  in  some  cases  a  chemical  change  occurs  only  when  heat 

is  added  to  the  changing  system  from  without  ;  in  such  a  case 


and  . 

This  equation  represents  an  endothermic  change. 

It  has  been  stated  that  if  an  exothermic  change  is  possible 
it  will  always  occur.  When  we  have  advanced  somewhat  in 
our  study  of  thermal  chemistry  we  shall  see  how  impossible 
it  is  to  found  a  system  of  classification  on  the  difference  be- 
tween exothermic  and  endothermic  changes.  In  some  cases, 
a  chemical  reaction  which  appears  to  be  accompanied  by 

1  Thomsen  appears  to  be  the  only  chemist  who  systematically  writes  the  indices 
above  the  symbols  of  elements  in  the  formulae  of  thermal  chemistry.  Thomsen 
also  sometimes  uses  the  colon  in  place  of  the  comma  to  express  chemical  reaction 
between  the  substances  whose  formulae  are  separated  by  this  symbol. 


§  119}  APPLICATION   OF   PHYSICAL  METHODS.  255 

absorption  of  heat  is  found,  on  more  careful  study,  to  form 
one  member  of  a  series  of  changes  the  thermal  sum  of  which 
is  represented  by  a  positive  quantity.  Indeed  any  chemical 
reaction  is  a  most  complex  phenomenon  when  regarded  from 
the  thermal  point  of  view ;  physical  changes  (expansion  or 
contraction,  passage  from  solid  to  liquid  or  gas,  or  vice  versa, 
&c.,  &c.)  form  part  of  the  total  change,  the  thermal  value  of 
which  is  set  down  in  a  lump  sum.  But  thermal  chemistry 
aims  at  something  more  than  this  rough  grouping  together 
of  positive  and  negative  values.  Thermal  chemistry  tries  to 
disentangle  the  primary  chemical,  from  the  subordinate  phy- 
sical changes,  and  moreover  to  divide  the  chemical  processes 
into  those  which  consist  of  molecular  decompositions,  and 
those  which  consist  of  atomic  combinations. 

It  is  not  possible  to  enter  on  any  full  discussion  of  the 
terms  exothermic  and  endothermic  as  applied  to  chemical 
phenomena  until  the  subject  of  affinity  has  been  treated ;  at 
present  I  wish  to  insist  on  the  inadvisability  of  making  the 
conception  implied  in  these  terms  the  basis  of  a  system  of 
classification  of  chemical  reactions,  and  at  the  same  time  to 
draw  attention  to  some  processes  which  are  suggested  by  the 
terms  in  question. 

Naumann1  shewed  that  no  action  occurs  when  dry  sul- 
phuretted hydrogen  is  passed  into  a  solution  of  iodine  in  dry 
carbon  disulphide,  but  that  as  soon  as  water  is  added,  hy- 
driodic  acid  and  sulphur  are  produced.  The  reaction 

2H2S  +  2l2  =  4HI  +  S2 

(gaseous)       (solid)    (gaseous)    (solid) 

would  be  thermally  represented  as 

[2H'S,2l*J-     4[H,I]-2[H*,S] 
=  -24800-9200 
=  -  34,000. 

When  water  is  present,  the  reaction 

2H2S     +     2l2     =     4HI     +     S2 

(in  solution)    (in  solution)     (in  solution)        (solid) 
1  Ber,  2.  177;  and  Anna/en  151.  145. 


256  CHEMICAL   STATICS.  [§  119 

would  be  thermally  represented  as 

[2H2SAq,  2l2Aq]=4[H,  I,  Aq]-2[H2,  S,  Aq] 
=  52,800-  18400 
=  34,400!  +  . 

The  reaction  of  dry  sulphuretted  hydrogen  on  dry  iodine 
would  be  markedly  endothermic;  but  when  this  change  is  made 
one  of  a  series  the  thermal  value  of  which,  taken  as  a  whole, 
is  positive,  then  the  complete  cycle  of  change  proceeds  rapidly. 

But  the  more  concentrated  an  aqueous  solution  of  hydri- 
odic  acid  becomes  the  less  heat  is  there  evolved  on  each 
addition  of  the  acid,  until  the  specific  gravity  of  the  liquid 
is  i'562,  after  which  no  more  heat  is  evolved;  the  liquid  is 
saturated.  If  therefore  the  hydriodic  acid  produced  in  the 
foregoing  reaction  is  allowed  to  accumulate  in  the  liquid,  no 
more  water  being  added,  a  point  will  be  reached  at  which  the 
sum  of  the  thermal  changes  is  equal  to  zero ;  at  this  point 
the  chemical  change  stops,  but  proceeds  again  on  the  addi- 
tion of  a  little  water.  It  is  possible  to  obtain  an  aqueous 
solution  of  hydriodic  acid  of  specific  gravity  1*67  ;  if  sulphur 
is  shaken  with  this  liquid  a  little  sulphuretted  hydrogen  and 
iodine  are  produced,  i.e.  the  change 

S2  +  4HI  =  2H2S  +   I2 

(solid)  (concentrated)  (solution)  (solution) 

proceeds  until  the  hydriodic  acid  becomes  reduced  to  specific 
gravity  1*56,  when  equilibrium  is  again  established. 

Portions  of  this  cycle  of  change  are  exothermic,  other 
portions  are  endothermic.  Variation  of  the  mass  of  one  of 
the  members  of  the  changing  system  determines  whether 
the  thermal  value  of  the  complete  change  shall  be  positive 
or  negative,  and  also  determines  the  direction  in  which  the 
change  shall  proceed.  This  reaction  may  be  taken  as  typical 
of  most  if  not  all  chemical  processes.  Such  processes  consist 
of  portions  having  positive  thermal  values  and  portions  having 
negative  values ;  small  variations  in  the  conditions  may 

1  No  notice  is  taken  in  these  thermal  expressions  of  the  change,  if  any,  which 
accompanies  the  decomposition  of  2l2  and  the  production  of  S2.    See /tor/,  par.  132. 

2  This  liquid  contains  about  25  per  cent,  of  HI. 


§  120]  APPLICATION    OF    PHYSICAL   METHODS.  257 

determine  whether  the  process  as  a  whole  shall  belong  to  the 
class  of  exothermic  or  to  that  of  endothermic  changes. 

1 20.  Direct  measurements  of  the  thermal  changes  which 
accompany  chemical  changes  can  only  be  made  in  a  few 
simple  cases ;  it  is  generally  necessary  to  have  recourse  to 
indirect  methods.  The  truth  of  the  following  deduction  from 
the  theory  of  energy  is  assumed  in  all  these  methods  of  calcu- 
lation. 

The  total  loss  of  energy  by  a  chemical  system  in  passing 
from  a  definite  initial  to  a  definite  final  state  is  independent 
of  the  intermediate  states. 

The  total  loss  of  energy  is  of  course  measured  by  the 
heat  evolved  and  the  work  done  by  the  system  in  its  pas- 
sage from  one  state  to  the  other.  But  for  our  purpose  the 
energy  given  out  in  forms  other  than  that  of  heat  may 
be  overlooked,  and  we  may  put  the  statement  in  this  form  ; 
the  total  thermal  change  during  a  chemical  process  is  de- 
pendent only  on  the  initial  and  final  states  of  the  chemical 
system. 

In  applying  this  statement,  it  is  necessary  to  arrange 
series  of  reactions  each  beginning  with  the  same  materials  in 
the  same  conditions  and  ending  with  the  same  products  under 
the  same  conditions  ;  all  the  processes  which  form  one  of  the 
cycles  of  change  must  be  capable  of  calorimetrical  measure- 
ment, and  all  the  processes  in  the  other  cycle,  except  that  one 
the  thermal  value  of  which  is  to  be  determined,  must  also  be 
capable  of  measurement  by  the  calorimeter  :  if  this  be  done, 
it  follows  from  the  principle  just  stated  that  the  difference 
between  the  total  thermal  values  of  the  two  cycles  of  changes 
represents  the  thermal  value  of  that  special  portion  of  one  of 
the  cycles  which  it  is  wished  to  determine.  Each  cycle  may 
however  consist  of  various  parts,  so  that  it  is  sometimes  a 
little  difficult  to  unravel  all  the  changes,  and  to  find  that 
portion  of  one  cycle  the  thermal  value  of  which  has  to  be 
determined  by  calculation. 

I  shall  now  give  some  examples  to  shew  how  the  thermal 
values  of  various  chemical  changes  are  deduced  from  the 
results  of  experiments. 

M.  c.  17 


258  CHEMICAL   STATICS.  [§  I2O 

A.  It  is  required  to  determine  the  thermal  value  of  the 
synthesis  of  CH2O2  from  C,  H2,  and  O2. 

We  start  with  12  grams  of  carbon,  2  of  hydrogen,  and 
48  of  oxygen  ;  these  combine  to  form  18  grams  of  water, 
and  44  grams  of  carbon  dioxide  (C  +  H2+  O3  =  CO2+  H2O). 
But  the  same  quantities  of  carbon,  hydrogen,  and  oxygen 
might  be  (theoretically)  combined  to  form  46  grams  of 
formic  acid,  which  could  then  be  oxidised,  by  16  grams  of 
oxygen,  to  form  18  grams  of  water  and  44  grams  of  carbon 
dioxide.  Stated  in  formulse  these  changes  are 

(i)  C  +  H2  +  02  =  CH202;        (2)  CH202  +  0  =  C02  +  H20. 

The  following  are  the  thermal  values  of  the  different  por- 
tions of  these  changes : 

[C,  02]  =  96,96o  +  :  [H2,  O]  =  68,36o  +  :  [CH2O2,  O]  =  65,900  + 
but  [C,  02]  +  [H2,  0]  =  [C,  H2,  02]  +  [CH202,  01=165,320  + 

/.  [C,  H2,  02]  =  [C,  02]  +  [H2,  0]-[CH202,  0]=  99420  +  . 

B.  A  rather  more  complicated  example  is  furnished  by 
the  determination  of  the  thermal  values  of  the  actions  (i) 
[H,  Br],  (2)  [H,  I];  i.e.  of  the  reactions  whereby  HBr  and 
HI  are  conceived  to  be  formed  from  their  elements. 

(i)  [H,  Br].     The  data  are 

[H,  Cl,  Aq]  =  39,30o;  [HBr,  Aq]=  19,900*: 

therefore  assuming  that 

[H,Br,Aq]  =  [H,Cl,Aq] 
it  follows  that 

[H,  Br]  =  39,300-  19,900=19,400. 

But  is  the  formation  of  an  aqueous  solution  of  HBr  from 
H,  Br,  and  water  attended  with  the  same  thermal  change 
as  accompanies  the  formation  of  an  aqueous  solution  of  HC1 
from  H,  Cl,  and  water?  Or,  if  this  assumption  is  not 
justified  by  facts,  what  is  the  difference  between  the  thermal 
values  of  the  two  changes  ? 

Now,  in  the  first  place,  the  thermal  values  of  the  formation 
of  KC1  and  KBr  in  aqueous  solution  are  equal,  i.e. 

[KOHAq,  HClAq]=[KOHAq,  HBrAq]. 
1  When  no  +  or  —  sign  is  given  it  is  to  be  understood  that  heat  is  evolved. 


§  120]  APPLICATION   OF   PHYSICAL   METHODS.  259 

But  the  replacement  of  Br  by  Cl  is  attended  with  a  consi- 
derable evolution  of  heat ;  the  data  here  are 
[KBrAq,  Cl]=  11,500. 

Now  if  we  analyse  this  change  we  find  that  the  thermal 
expression  when  expanded  becomes 

[K,  Cl,  Aq]  +  [Br,  Aq]-[K,  Br,  Aq]- 11,500: 
but  [Br,  Aq]  =  5oo: 

.'.  [K,  Cl,  Aq]-[K,  Br,  Aq]=  11,500-  500=  11,000. 

That  is  to  say,  the  replacement  of  Br  by  Cl  in  aqueous  solu- 
tion is  represented  by  the  thermal  value  11,000  units,  and  as 
the  heat  of  neutralisation,  in  aqueous  solution,  of  KOH  by 
HC1  is  equal  to  that  of  KOH  by  HBr,  it  follows  that 

[H,  Br,  Aq]  =  [H,  Cl,  Aq]  -  1 1 ,000  =  28,300  : 
and  as  [HBr,  Aq]  =  19,900,  it  follows  that  [H,  Br]  =  8,400. 

(2)   [H,  I].    The  data  are 

[H,  Cl,  Aq]  =  39,3oo;   [HI,  Aq]- 19,200. 

Now 

[KOHAq,  HIAq]  =  [KOHAq,  HClAq]  -  70  : 
also 

[KIAq,  Cl]  =  26,200  (iodine  separating  as  solid) : 

/.  replacement  of  I  by  Cl  is  accompanied  by  evolution  of 
26,200  -  70  =  26,130  units  : 

.'.  [H,  I,  Aq]  =  [H,  Cl,  Aq]- 26,130=  13,170  : 
and  as  [HI,  Aq]=  19,200 

it  follows  that  [H,  I]=  -6,030. 

C.  The  heat  of  formation  of  H2SO4  from  its  elements,  i.e. 
the  thermal  value  of  the  change  [H2,  S,  O4],  has  been  calcu- 
lated by  Berthelot.  Thus, 

(a)  oxidation  of  sulphurous  acid  in  aqueous  solution  by 
chlorine ; 

[H2S03Aq,  H20,  Cl2]  =  73,9oo: 

this  expression  when  expanded  becomes, 

73,900  =  2  [H,  Cl,  Aq]  +  [H2S03Aq,  O]-[H2O]. 

17—2 


260  CHEMICAL  STATICS.  [§  I2O 

But  2[H,  Cl,  Aq]  =  78,600  :  and  [H2,  O]  =  68,400  : 

/.  [H2S03Aq,  0]  =  73,900  -(78,600  -68,400)  -63,700+  .........  (i) 

(b)    [SO2,  Aq]  =7,700: 

but,  assuming  that  when  SO2  is  dissolved  in  water  the  solution  contains 
H2SO3,  it  follows  that 

[SO2,  Aq]=[H20,  SO2,  Aq]  : 
/.  from  (i)  [SO2,  H2O,  O,  Aq]  =  63,700  +  7,700  =7  1,400+  ......  (2) 

to    [S,  02]=69,ooo: 

/.  from  (2)  [S,  O2,  O,  H2O,  Aq]  =  7  1,400  +  69,900  =141,  300  +...(3) 


now,  dividing  (3)  into  two  parts,  we  have 

part  («)...  [S,  O2,  O],  and  part  (£)...  [SO3,  H2O,  Aq]; 
but  we  know  the  value  of  part  (£),  and  also  the  total  value, 

/.[S,  O2,  O],  i.e.  [S,  O3],  =  i4i,3oo-37,4oo=io3,9oo  ......  (4) 

to     [H2S04,Aq]=  17,000: 
Now  we  have  the  values, 
(a)    [S,  03]=  103,900:   (£)[S03,  H20]  =  ?:    (c)  [H2SO4,  Aq]=  17,000: 


/.[SO3,  H2O]  =  20,400. 
But[S,  O3]=io3,9oo;  /.[S,  O3,  H2O]=  103,900  +  20,400  =124,300... 

-(5) 
(/)    but  [H2,  0]=68,4oo: 

.-.  from  (s)  [S,  O2,  0,  H2,  O]   i.e.   [S,  O4,  H2]=  124,300+68,400 

=  192,700  +  . 

The  calculation  of  so-called  heats  of  formation  are  all 
based  on  the  principle  we  are  now  discussing. 

D.  Thus,  required  the  heat  of  formation  of  methane 
(CH4).  We  start  with  the  two  systems  (i)  C  +  H4,  (2)  CH4. 
Each  is  completely  oxidised  to  the  same  final  products,  viz. 
CO2  +  2H2O;  the  difference  between  the  quantities  of  heat 
evolved  in  these  two  changes  is  called  the  heat  of  formation 
of  CH4.  Thus, 

[C,  O2]  =  96,9oo:  2[H2,  O]=  136,800:  sum  =  233,700 
but  [CH4,  O4]=2i3,5oo 

.'.    [C,  H4]=    20,200  +  . 


§  1  20]  APPLICATION   OF  PHYSICAL  METHODS.  26  1 

As  it  is  important  that  a  definite  meaning  should  be 
attached  to  the  expression  *  heat  of  formation,'  a  few  more 
examples  are  given. 

E.  Required  the  thermal  value  of  the  reaction  [H,  C,  N], 
that  is,  of  the  reaction  whereby  HCN  may  be  conceived  to  be 
formed  from  its  elements. 

Data;  [C,  O2]=  96,900:  |[H2,  O]=  34,200:  sum=  131,100  (N  is  in- 
combustible) but  [CNH,  |O]=  1  59,500 

.-.  [C,N,H]i=  28,400-. 

F.  Required  the  thermal  value  of  the  reaction  [N2,  0]. 

Data;  the  reaction 

C  +  2N2O  =  2N2  +  CO2  when  expanded  thermally  is 
[C,  2N20]=[C,  02]-2[N2,  0]=  133,900: 
but 


•••  2[N2,  0]  =  37,000- 
.'.     [N2,0]  =  18,500-. 

G.     Required  the  thermal  value  of  the  reaction  [N,  O]. 

Data;  CN  +  2NO  =  CO2  +  3N,  or  in  thermal  notation 

[CN,  2NO]  =[C,  01  -[C,  N]-2[N,  0]=i74,6oo: 
but  CN  +  O2  =  CO2  +  N 
=[C,02]-[C,N]=  130,900: 
.-.  2[N,0]=43>7oo-: 
.-.     [N,  O]=2i,85o-. 

H.     Required  the  thermal  value  of  the  reaction 

C2H60  +  C2H402  =  (C2H5)C2H302  +  H2O  ; 
or  in  thermal  notation 

[C2H60,  C2H402]. 

Data;  [C2H6O,  O6]  = 

[C'H«0«,  04] 
but  [(C2H5)C2H302,  010]= 

[H20,  0]=o 
/.  [C2H60,  C2H402]= 

1  The  transference  of  N  from  the  molecule  N2  to  the  molecule  HCN  is  assumed 
to  be  accompanied  by  no  thermal  change.     See/w/  par.  132. 


262  CHEMICAL   STATICS.  [§  I2O 

The  heat  of  formation  of  a  substance  will  of  course  vary 
according  as  the  substance  is  formed  in  the  gaseous,  liquid, 
or  solid  state,  and  also  according  to  the  temperature  of 
formation.  The  following  examples  will  illustrate  this. 

I.  Required  the  thermal  value  of  the  formation  of 
aldehyde  from  its  elements,  i.e.  of  the  reaction  [C2,  H4,  O], 
when  the  aldehyde  is  (a)  liquid,  (b)  gaseous. 

(a)  Liquid  :  data, 


2 

(liquid)  (liquid) 

i.e.  [C2H40,  05]  =  2[C,  02]  +  2[H2,  O]-[C2,  H4,  O]  =  275,500 
but  2  [C,  O2]  +  2  [H2,  O]  =  330,600 

.-.  [C2,  H4,  O]  liquid1^   55,100  +  . 
(l>)  Gaseous  :  data, 

[C2H4O,  O5]  =  266,000;  and  2  [H2,  O]=  117,400  : 

(gaseous)  (gaseous) 

.-.  [C2,  H4,  O]  gaseous  =45,  200. 

K.  If  the  products  of  a  reaction  are  gaseous  and  are 
maintained  at  a  high  temperature,  it  becomes  necessary  to 
introduce  corrections  for  the  specific  heats,  and  heats  of 
vaporisation,  of  these  products,  into  the  calculation  of  the 
thermal  value  of  the  reaction. 

Thus,  required]  the  thermal  value  of  the  reaction  [CaH2,  O5] 
at  150°. 


Data,  C2H2  +  06  =  2C02  +  H20,  [or  C2H2,  O5] 

(liquid) 

at  ordinary  temperatures  (2o°)  =  2[C,  O2]  +  [H2,  O]-[C2,  H2]  =  3io,6oo  : 
but  thermal  capacity  of  2  gram-molecules  of  CO2  for  tem- 

perature-interval 20°  —  150°  .........         =  2482  units. 

(a)  i  mol.  liquid  H2O  20°—  1  00°  =  18.80=   1440    „ 


thermal  capacity  of 
i  gram-molecule 
of  H2O 


(£)  heat  of  vaporisation  of  do.  at  100° 

=  18.536-5  =  9657 

(c)  thermal  capacity  of  i  mol.  steam 

100° — 1 50°  =18.50.0-4805  =  432 


units. 


1  The  CO2  produced  is  gaseous  ;  the  heat  of  formation  of  liquid  CO2  is  un- 
known. 


§  I2O]  APPLICATION    OF   PHYSICAL   METHODS.  263 

.-.  [C2H2,  O6]  at  i5o°  =  3io,6oo- 14,011  =  296,589  (say  296,600) 
gram-units. 

The  thermal  values  of  reactions  of  various  kinds  may  be 
determined  by  the  use  of  the  principle  laid  down  in  par.  120. 
The  following  are  examples. 

L.  The  heat  of  liquefaction  of  the  hydrate  H2SO4.  H2O 
is  found  to  be  —  3680  from  these  data, 

[H2SO4H2O,  Aq]  =  ;i2o  :         [H2SO4H2O,  Aq]=  10,800. 

(solid)  (liquid) 

M.  The  mean  thermal  value  of  the  fixation  of  each 
molecule  of  water  by  a  salt  when  undergoing  hydration  may 

be  found  by  using  the  formula  — ; 

where  Ztf  =  heat  of  solution  of  dehydrated  salt, 

Ln=  „  hydrated  salt  with  n  molecules  of  water, 

thus,  for  Na2SO4J 

Z<,  =  46o  units  +  .  Ln=   1,900  units-,  when  n=  i : 

»  =  4,365  „  -j  „  ^  =  2-4: 
„  =10,100  „  -,  „  ;z  =  5'4: 
„  =18,800  „  -,  „  n  =  io. 

Hence,  calculating  from  the  salt  Na2SO4.  ioH2O,  the  mean 
thermal  value  of  the  reaction  [Na2SO4,  H2O]  is  —  1834  units; 
and  calculating  from  the  salt  Na2SO4.  5*4  H2O,  the  mean 
value  for  the  same  reaction  is  —  1785  units. 

If  the  heat  of  liquefaction  of  water  is  subtracted  from 
the  difference  L0  —  LH,  we  get  the  thermal  value  of  the  com- 
bination   with   solid    water   of  the    salt  in  question.     Thus, 
taking  sodium  butyrate, 
for  C4H7NaO2;  £,=4240  units: 

and  for       C4H7NaO2.3H2O  ;  £,,  =  3440    „     :     .'.  L0-Ln  =  800  units  ; 
but  heat  of  liquefaction  of  3  gram-molecules  water  =  -  1430.3=  -4290: 

800  -  ( -  4290) 
hence-     -±—2     -'=-1697: 

i.e.  the  mean  thermal  value  for  the  combination  of  each 
molecule  of  water,  in  the  solid  form,  with  C4H7NaO2  is  repre- 
sented by  -  1697  gram-units. 

N.  The  heat  of  formation  in  solution  of  a  double  salt, 
is  the  difference  between  the  heat  of  solution  of  the  double 


264  CHEMICAL   STATICS.  [§  I2O 

salt,  and  the  sum  of  the  heats  of  solution  of  its  constituents  ; 
thus, 

TJ     ».  _r         Heat  of  forma- 
jieat OI        j.- 
Double  salts.  solution 

K2SO4          6340  -\  KS  11-260- 

CuSO4.5H2O    2430-} 

(NH4)2SO4.CuSO4.7H2O    11240-          6860-. 


O.  One  other  example  of  the  calculation  of  a  heat  of 
formation  will  be  given,  as  it  serves  to  shew  how  very  indi- 
rect are  the  methods  sometimes  adopted. 

Required  the  thermal  value  of  the  reaction  [Cl2,  O]. 

Data,  (i)  for  finding  the  value  of  [H,  Cl,  O,  Aq]  : 


(a)  the  reaction  2NaOH  +  Cl2  =  NaCl  +  NaClO  +  H2O,  if  expanded 
thermally  becomes 

[2NaOH,  C12]  =  [H,  Cl,  Aq]  +  [H,  Cl,  O,  Aq]-[H2,  O] 

+  [NaOHAq,  HClAq]  +  [NaOHAq,  H  CIO  Aq]  =  24,600  : 
but  [H,  Cl,  Aq]  =39,300 

[H2,  O]  =  68,400 
[HClAq,  NaOHAq]=  13,700 
[HClOAq,  NaOHAq]=  10,000  ; 

.-.  24,600  =[H,  Cl,  O,  Aq]  +  39,  300  +13,700  +10,000  -68,400 

[H,  Cl,  O,  Aq]-  5,400: 
.'.  [H,  Cl,  O,  Aq]  =  30,000. 

(b)  the  decomposition   of  aqueous   HC1O   by  aqueous   HI,   viz. 
2HI  +  HC1O  =  HC1  +  H2O  +  I2,  if  expanded  thermally  becomes 
[HClOAq,  2HIAq]=[H,  Cl,  Aq]  +  [H2,  O]-[H,  Cl,  O,  Aq] 

-2[H,  I,  Aq]  =  Si,4oo: 

but  [H,Cl,Aq]  =  39,300 

[H2,0]^  68,400 
2[H,  I,  Aq]  =  26,350: 

,-.  51,400=81,350  -[H,  Cl,  O,  Aq]  : 
.-.  [H,  Cl,  O,  Aq]  =  29,95o. 
Hence  mean  value  of  [H,  Cl,  O,  Aq]  =  (29,975)  say  30,000. 

(2)    Further  data  for  finding  [Cl2,  O]  : 

the  reaction  C12O  +  H2O  =  2HC1O,  if  expanded  thermally  becomes 
[C120,  H20]  =  2[H,  Cl,  O,  Aq]-[H2,  O]-[C12,  O]-94oo. 


§  I2l]  APPLICATION    OF   PHYSICAL   METHODS.  265 

But  we  have  already  found 

2  [H,  Cl,  O,  Aq]  =  6o,ooo  :  and  [H2,  O]=68,4oo  : 
.-.  9,400=-  8,400  -[Cl2,  O] 
.-.  [CP,0]=-  17,800. 

121.  From  these  examples  we  may  provisionally  conclude 
that  a  chemical  change  which  is  accompanied  by  considerable 
loss  of  energy  to  the  changing  system  will  generally  occur 
unless  prevented  by  actions  outside  of  the  system. 

The  following  processes  may  be  taken  as  illustrative  of 
this  somewhat  vague  generalisation. 

The  acids  of  the  acetic  series  readily  yield  chloro-,  or 
bromo-derivatives  by  the  direct  action  on  them  of  chlorine  or 
bromine,  iodine  however  does  not  react  under  similar  con- 
ditions to  form  iodo-acids.  The  thermal  values  of  the  reac- 
tions of  the  three  halogens  on  acetic  acid  are  as  follows, 

X=Cl  =  30,000  units  +. 


(^r=i  =18,000   „    -. 
The  reverse  action  in  the  case  of  iodine,  viz. 

C2H3I  O2  +  H  I  =  C2H4O2  +  12 
is  represented  thermally  thus, 

[CWIO2,  HI]=  18,000. 

This  action  occurs  provided  a  concentrated  aqueous  solu- 
tion of  hydriodic  acid  is  employed. 
Now 


(gas)  (solid) 

=  -2[H,l] 
=  12,400. 

But  [2HI,  Aq]  =  38,000: 

hence  it  follows  that  the  decomposition  of  2HI  into  H2  +  I2 
in  dilute  solution  would  absorb  38,000—  12,400  =  25,600  units 
of  heat. 

These  thermal  numbers  shew  that  the  process  which 
is  accompanied  by  a  large  loss  of  energy  occurs,  whereas 
that  which  would  involve  gain  of  energy  to  the  system  does 
not  occur. 

But  why  does  a  concentrated  aqueous  solution  of  hydriodic 
acid  act  as  an  energetic  reducing  agent  ?  We  have  already 


266  CHEMICAL   STATICS.  [§  121 

learned  (par.  119)  that  little  or  no  heat  is  evolved  during  the 
absorption  and  solution  of  gaseous  hydriodic  acid  by  a  solu- 
tion of  that  gas  containing  about  20 — 25  per  cent,  of  HI ; 
hence  a  concentrated  solution  of  this  compound  contains 
a  considerable  quantity  of  HI,  as  distinguished  from 
HI.;rH2O.  But  the  numbers  given  above  shew  that  HI 
contains  much  more  energy  than  HI.^rH2O;  hence  a  con- 
centrated aqueous  solution  of  hydriodic  acid  is  much  more 
energetic  than  a  dilute  solution  of  the  same  compound1. 

The  following  tables2  contain  thermal  data  for  discussing 
the  action  of  sulphuretted  hydrogen  as  a  reagent  for  precipi- 
tating certain  metals  from  acid  solutions,  and  other  metals 
only  from  neutral  or  alkaline  solutions. 

TABLE  I. 

Base 


Reaction  CdO      PbO     CuO     HgO     T12O     Cu2O    Ag2O 
[Base  2HClAq, }  .  N 

H2SAq]        J  ^  27'3°°  29>2°°  3I)7°°  45'3°°  3  '5°°  3  )5°°  5  '5°° 

^  2°'3°°  I5'4°°  I5'3°°  I9'°°°  27'5°°  I4'7°°  42'6°° 


(i)-(2)=+  7,000  13,800  16,400  26,300  11,000  23,800  15,900 

TABLE  II. 

Base 

Reaction  'CdO       PbO       CuO       HgO      T12O       Cu2O     Ag2O 

[Base,  H2S]     (i)  32,100    34,000    36,500    50,000     43,300    43,300    63,300 
[Base,  2HC1]  (2)  55,000    50,000    50,000     53,500     62,200    49,300   77,200 

(i)- (2)= -22,900    16,000    13,5°°      3>5°°     18,900     6,000    13,900 

TABLE  III. 

Base 


Reaction              MnO.H2O  FeO.H2O  NiO.H2O  CoO.H2O  ZnO.H2O 
[Base  2HClAq, }   ,  N 

H2SAq]       J    ^     I0'7°°         I4'                  '               I7'4°°  I8'6°° 
[Base  Aq,      }    .  x 

2HClAq]      J    ^    23'°°°        2I'4°°        22'               2I>I°°  20'3°° 

(i)- (2)= -12,300          6,800          4,000          3,700  1,700 

1  See  Naumann,  Thermochemie,  495  and  501. 

2  See  Naumann,  loc.  cit.  505 — 510. 


§  121]  APPLICATION   OF   PHYSICAL   METHODS.  267 

To  illustrate  the  application  of  these  data,  take  the  case  of 

cadmium. 

[Cd02HClAq,  H2SAq]  =  27,300  : 

i.e.  the  thermal  value  of  the  change  which  occurs  when  aqueous 
H2S  reacts  on  a  dilute  solution  of  CdO  in  HC1  is  represented 
by  27,300  units  +. 

[CdOAq,  2HClAq]  =  20,30o  : 

i.e.  the  thermal  value  of  the  change  which  occurs  when  CdO 
in  aqueous  solution  is  neutralised  by  a  dilute  solution  of  HC1 
is  represented  by  20,300  units  -f.  The  former  number  exceeds 
the  latter  by  7,000,  .'.  the  action  of  H2S,  in  solution,  on  CdO, 
in  dilute  HC1  solution,  is  accompanied  by  evolution  of  7,000 
units  of  heat ;  this  action  readily  occurs.  But 

[CdO,  H2S]  =  32,100;   and  [CdO,  2HC1]  =  55,000  : 

i.e.  the  formation  of  CdS,  by  the  action  of  gaseous  H2S  on 
CdO,  is  accompanied  by  the  evolution  of  22,900  units  of 
heat  less  than  attends  the  action  of  gaseous  HC1  on  CdO, 
/.  CdS  is  decomposed  by  gaseous  HC1  with  formation  of 
CdCl2. 

Moreover  the  numbers 

[2HC1,  Aq]  =  34,600  ;  whereas  [H2S,  Aq]  =  4,800 

shew,  that,  comparing  equivalent  quantities  of  hydrochloric 
acid  and  sulphuretted  hydrogen,  the  former  when  in  the  state 
of  gas  possesses  an  excess  of  energy,  measured  by  about 
34,000  thermal  units,  above  what  it  possesses  when  in  dilute 
solution,  whereas  the  excess  of  energy  of  gaseous  H2S  above 
that  possessed  by  H2S .  ^H2O  is  measured  by  about  5000 
thermal  units.  But  the  more  concentrated  an  aqueous  solu- 
tion of  hydrochloric  acid,  the  less  is  the  quantity  of  heat 
evolved  by  adding  hydrochloric  acid  gas  to  that  solution; 
in  other  words,  a  concentrated  aqueous  solution  of  this  acid 
is  nearly  as  energetic  a  reagent,  provided  it  is  used  in  suffi- 
cient quantity,  as  gaseous  hydrochloric  acid.  Hence  we 
should  conclude,  and  our  conclusion  is  verified  by  experiment, 
that  cadmium  sulphide  will  be  decomposed  by  concentrated 
aqueous  hydrochloric  acid. 


268  CHEMICAL  STATICS.  [§  122 

The  case  of  antimony  is  especially  interesting. 

Antimony  sulphide  is  decomposed  by  aqueous  hydrochlo- 
ric acid  of  greater  concentration  than  HC1.6H2O  ;  but  if  more 
water  than  this  is  present,  antimony  chloride  is  decomposed 
by  sulphuretted  hydrogen.  Hence  the  two  reactions 

Sb,S8+6HCl=2SbCl8+3H2Sl 


may  occur  until  a  state  of  equilibrium  is  established,  which 
is  conditioned  by  the  relative  energies  of  the  components,  and 
this  again  is  conditioned  by  the  relative  masses  of  these  com- 
ponents, temperature  being  constant  throughout. 

A  consideration  of  Table  III.  shews,  that  the  heat  of 
neutralisation  by  2HC1  of  any  of  the  bases  in  that  table  is 
greater  than  the  heat  evolved  during  the  action  of  H2S  on 
such  neutralised  solutions;  we  should  not  therefore  expect 
sulphuretted  hydrogen  to  precipitate  the  metals  in  this  table 
from  dilute  acid  solutions.  But  if  ammonia  (or  soda)  is  added 
to  such  solutions,  the  hydrochloric  acid  is  neutralised  rather 
than  the  sulphuretted  hydrogen,  because 

[(NH4)2OAq,  H2SAq]  =  6,30o:  but  [(NH4)2OAq,  2  HClAq]  =  24,700. 
Under  these  conditions  the  base  is  precipitated  as  sulphide1. 

The  energetic  action  of  antimony  pentachloride  as  a  chlo- 
rinating agent  is  in  keeping  with  the  thermal  values  obtained 
by  Thomsen2,  viz. 

[Sb,  Cl3]  =  9i,4oo;  but  [SbCl3,  Cl2]-  13,500. 

These  numbers  shew  that  the  formation  of  the  molecule  SbCl5, 
from  SbCl3  and  C12,  is  attended  with  a  loss  of  energy  much  less 
than  two-thirds  of  that  lost  in  the  formation  of  the  molecule 
SbCL  from  Sb  and  CL. 

o  o 

122.  We  have  been  accustomed  to  regard  most  processes 
of  chemical  change  as  consisting  of  two  parts,  (i)  decomposi- 
tion of  the  molecules  forming  the  initial  system,  (2)  rearrange- 
ment of  the  atoms  thus  produced  to  form  the  new  molecules 
which  compose  the  final  system.  The  first  part  of  a  change, 

1  For  more  details  see  Naumann,  loc.  cit. 

2  See  Thermochemische  Untersuchungen,  2.  332  —  4. 


§  123]  APPLICATION    OF   PHYSICAL   METHODS.  269 

as  thus  regarded,  must  be  accompanied  by  gain  of  energy  to 
the  entire  system,  and  the  latter  part  by  loss  of  energy.  The 
gain  may  exceed  the  loss,  or  vice  versa;  the  process  as  a 
whole  may  be  endothermic  or  exothermic.  In  the  preceding 
paragraphs  of  this  section  no  attempt  has  been  made  to 
separate  the  thermal  values  of  these  two  parts  of  any  change, 
the  numbers  given  in  these  paragraphs  represent  the  al'gebraic 
sums  of  two  or  more  quantities.  In  some  cases  the  chemical 
changes  are  represented  in  formulae  which  are  undoubtedly 
molecular,  but  in  most  cases  we  have  dealt  with  solid  or 
liquid  substances,  and  the  thermal  values  assigned  to  the 
various  changes  must  therefore  be  generally  regarded  as  only 
measuring  the  quantities  of  heat  evolved  or  absorbed  during 
the  reactions,  as  defined  in  the  equations,  between  those 
masses  of  the  various  chemical  substances  which  are  ex- 
pressed by  their  formulae  when  read  in  grams. 

But  if  relative  measurements  of  the  gains  of  energy  which 
accompany  the. formation  of  atomic,  from  molecular  systems, 
could  be  obtained,  much  light  would  certainly  be  thrown  on 
many  questions  which  have  been  discussed  or  alluded  to  in 
preceding  chapters. 

123.  Thomsen1  has  attempted  to  calculate  the  quantity 
of  heat  required  to  separate  the  molecule  of  carbon,  as- 
sumed to  be  diatomic,  into  atoms ;  his  results  and  methods 
will  be  discussed  hereafter  (par.  134).  Meanwhile  we  may 
note  that  what  Thomsen  calls  the  '  heat  of  dissociation '  of  a 
carbon  atom  is  supposed  to  be  equal  to  about  37,000  gram- 
units. 

E.  Wiedemann2  has  measured  the  heat  required  to  change 
the  '  band  spectrum '  of  hydrogen  into  the  '  line  spectrum  ' ; 
and,  on  the  assumption  that  the  '  line  spectrum '  is  associated 
with  vibrations  of  atoms  and  the  '  band  spectrum '  with 
vibrations  of  molecules,  he  has  calculated  that  about  128,000 
gram-units  of  heat  are  required  in  order  to  separate  I  gram- 
molecule  of  hydrogen  into  its  constituent  atoms ;  and  that 

1  Ber.  13.  1321  and  1388.    Do.  15.  328.     See  also  Thermochemische  Untersuch- 
ungen,  2.  101  et  seq. 

'2   Wied.  Ann.  [-2]  5.  500,  and  do.  18.  509. 


2/0  CHEMICAL   STATICS.  [§  124 

a  greater  quantity  of  heat  than  this  is  required  in  the  case  of 
the  molecule  of  nitrogen. 

Thomsen  and  Wiedemann  have  shewn  that  more  energy 
is  almost  certainly  associated  with  a  mass  of  hydrogen, 
nitrogen,  or  gaseous  carbon,  when  the  greater  part  of  the 
matter  is  in  the  state  of  atoms  than  when  in  the  state  of 
molecules ;  in  other  words,  their  investigations  furnish  physi- 
cal evidence  in  favour  of  the  generally  adopted  explanation 
of  nascent  actions. 

124.  The  actions  of  metals  on  acids  were  considered  in 
Chap.  II.  pars.  42  to  44.  Thermal  measurements  help  to 
elucidate  these  actions. 

If  the  heats  of  formation  in  aqueous  solution  of  the  sul- 
phates of  silver,  thallium,  copper,  cadmium,  mercury,  nickel, 
cobalt,  iron,  manganese,  and  zinc,  are  compared  with  the 
heat  of  formation  of  sulphuric  acid  in  aqueous  solution,  it  is 
found  that  the  former  values  are  greater  than  the  latter  except 
in  the  cases  of  copper  and  silver :  i.e.  for  the  heavy  metals 

[M(or  M2),  O2,  SO2,  Aq]  >  [H2,  O2,  SO2,  Aq], 

except  when  M  =  Cu  or  M2  =  Ag2 ;  hence  we  should  expect 
the  heavy  metals,  except  copper  and  silver,  to  decompose 
dilute  sulphuric  acid  with  evolution  of  hydrogen. 

When  M2  =  T12  the  positive  value  of  the  difference  in 
question  is  not  large  (1,900  units),  hence  the  action  between 
this  metal  and  dilute  sulphuric  acid  does  not  proceed  rapidly. 
But  when  the  acid  is  concentrated  action  is  more  energetic, 
inasmuch  as  the  heat  of  solution  of  H2SO4  is  large  ; 

[H2SO4,  Aq]  =  i7,ooo. 

But  as  a  given  mass  of  concentrated  sulphuric  acid  contains 
considerably  more  energy  than  the  same  mass  of  dilute  acid, 
it  follows  that  the  concentrated  acid  will  probably  be  less 
chemically  stable  than  the  dilute. 

The  action  of  thallium  on  the  concentrated  acid  results  in 
the  production  of  some  sulphur  dioxide.  Now  the  change 
H2SO4+ H2=SO2  +  2H2O  (assuming  that  this  expresses  the 
origin  of  the  sulphur  dioxide)  is  accompanied  by  the  evolii- 


§  124]  APPLICATION   OF   PHYSICAL   METHODS.  2/1 

tion  of  14,900  units  of  heat.      This  change  is   represented 
thermally  thus, 

[H2S04,  H2]  =  [S,  02]  +  2[H2,  0]-[S,  O2,  O2,  H2] 
=  2[H2,  0]-[S02,  O2,  H2]. 

If  the  temperature  is  raised  the  acid  becomes  more  concen- 
trated, and  at  a  certain  stage  sulphuretted  hydrogen  is 
evolved.  This  action  is  thermally  probable,  because 

[iH2S04,  H2]  =  [H25  0]  +  i[H2,  S]-i[H2,  S,  O4] 
=  [H2,  O]-1[H2S,O4] 
=  23,700  units +  . 

A  similar  treatment  of  the  action  of  copper  on  sulphuric 
acid  shews  that  this  metal  would  probably  not  decompose 
the  acid  when  dilute,  but  that  the  metal  might  be  expected 
to  react  slowly  on  concentrated  acid,  provided  one  of  the 
products  were  sulphur  dioxide  ;  because 

Cu  +  ;zH2SO4=CuSO4+SO2  +  2H2O  +  («  -  2)  H2SO4 
when  expanded  thermally,  is 

[Cu,  SO2,  O2]  +  2[H2,  O]-2[H2,  O2,  SO2] 
=  4,500  units +  . 

The  quantity  of  heat  set  free  in  this  action  will  in  reality 
considerably  exceed  5000  units,  because  heat  will  be  evolved 
by  the  action  between  the  H2SO4  and  2H2O  produced  in  the 
change ;  the  amount  of  heat  thus  liberated  may  amount  to  as 
much  as  8,000  or  9,000  units  per  gram-molecule  of  water. 

The  fact  that  H2SO4  and  H2O  combine  to  form  a  series  of 
hydrates,  the  production  of  each  of  which  is  marked  by  the 
evolution  of  heat,  complicates  such  calculations  as  those 
given  above.  The  relations  between  the  masses  of  H2SO4 
and  H2O  employed  will  certainly  condition  the  direction 
and  progress  of  the  change.  Starting  with  the  system 
H2SO4.^H2O-|-^H4,  for  a  certain  concentration  of  acid  the 
final  configuration  will  be  SO2  and  H2O,  for  another  concen- 
tration of  acid  it  will  rather  be  H2S  and  H2O,  or  SO2,  H2S 
and  H2O.  The  action  will  also  of  course  be  conditioned  by 
temperature. 


2/2  CHEMICAL   STATICS.  [§  124 

If  the  foregoing  considerations  are  correct,  it  follows 
that  any  metal  which  decomposes  dilute  sulphuric  acid  with 
evolution  of  hydrogen,  ought,  under  certain  conditions  of 
temperature  and  concentration  of  acid,  to  decompose  this 
acid  with  production  of  sulphuretted  hydrogen  or  sulphur 
dioxide  :  zinc  and  tin  certainly  do  produce  both  of  these 
gases  by  their  action  on  hot  concentrated  sulphuric  acid. 

A  comparison  of  the  heats  of  formation  of  nitrates  of  the 
heavy  metals  with  the  heat  of  formation  of  nitric  acid,  leads 
to  the  expectation  that  these  metals,  with  the  exception  of 
silver,  lead,  thallium,  copper  and  mercury,  would  decompose 
dilute  nitric  acid  with  production  of  hydrogen;  but  as  the 
excess  of  heat  evolved  in  this  decomposition  over  that  ab- 
sorbed in  separating  HNO3Aq  into  NH3,  NO,  NO2,  &c.  is 
large,  we  should  expect  the  gaseous  products  of  the  reaction  to 
consist  for  the  most  part  of  these  compounds.  The  statement 
may  be  put  thus  ;  the  initial  system  is  metal  and  dilute  nitric 
acid  ;  the  final  possible  system  is  metallic  nitrate,  oxides  of 
nitrogen  (or  ammonia),  and  water  ;  an  intermediate  stage  is 
metallic  nitrate  and  hydrogen  ;  in  the  passage  to  the  final 
system  much  more  energy  is  lost  than  if  the  change  stopped 
at  the  intermediate  stage,  therefore  the  change  proceeds  to 
what  may  be  called  its  natural  close. 

If  copper,  mercury,  or  silver  could  act  on  dilute  nitric  acid 
so  as  to  withdraw  a  portion  of  the  oxygen  of  the  acid,  such 
action  would  be  accompanied  by  a  considerable  loss  of  energy, 
and  would  therefore  be  thermally  probable.  The  formation 
of  nitric  oxide  would  absorb  more  heat  than  that  of  any 
other  possible  product  of  this  change  ;  but  the  necessary 
amount  of  heat  is  evolved  in  the  action  of  copper,  or  mercury, 
on  dilute  nitric  acid  ;  therefore  the  change 


is  thermally  possible,  assuming  the  first  part  to  consist  of  a 
deoxidising  action  of  copper  on  the  acid.  The  occurrence  of 
a  similar  change  when  copper  or  mercury  is  replaced  by  silver 
becomes  thermally  probable  only  when  the  acid  is  tolerably 
concentrated. 


§  125]  APPLICATION   OF    PHYSICAL   METHODS.  273 

Thermal  measurements  appear  then  to  indicate  differences 
between  the  action  of  zinc,  magnesium,  nickel,  &c.,  and  that 
of  copper,  mercury,  and  silver,  on  dilute  nitric  acid.  The 
gaseous  products  of  the  action  of  the  first  class  of  metals  are 
probably  for  the  most  part  the  results  of  secondary  changes 
occurring  between  nascent  hydrogen  and  the  acid,  whereas 
the  same  substances  when  arising  from  the  action  of  metals  of 
the  second  class  may  rather  be  regarded  as  the  results  of  a 
direct  deoxidising  action  exerted  by  the  metal  on  the  acid1. 

Traube,  as  we  found  in  chapter  u.  (pars.  43,  44),  from 
investigations  conducted  on  lines  very  different  from  those  of 
thermal  chemistry,  was  led  to  regard  the  action  of  copper  on 
nitric  acid  as  essentially  a  deoxidising  action. 

125.  From  what  we  have  learned  regarding  atomic  and 
molecular  systems,  and  from  a  consideration  of  the  preceding 
paragraphs  of  this  section,  it  follows  almost  necessarily  that 
change  from  one  allotropic  modification  of  an  element  to 
another  must  be  accompanied  by  absorption  or  evolution  of 
heat.  A  few  thermal  measurements  are  given  here  to  shew 
that  this  conclusion  is  fully  justified  by  facts. 

A.  [P2,  O5]  =  369,ioo  units+  when  P2  is  62  grams  of  ordinary 

phosphorus  (P«)  ; 
[P2,  O6]  =  326,8oo  units  +  when  P2  is  62  grams  of  amorphous 

phosphorus  (P0)  ; 

/.  the  change  of  Pa  to  P^=  21,150  units  of  heat  -f. 

In  the  oxidation  of  31  grams  Pa  to  H3PO4  in  aqueous  solution  by  hypo- 
chlorous  acid,  209,500  thermal  units  are  evolved  ; 

in  the  oxidation  of  31  grams  P0  to  H3PO4  in  aqueous  solution  by  hypo- 
chlorous  acid,  181,200  thermal  units  are  evolved  ; 

/.  the  change  of  Pa  to  P^  =  28,300  units  of  heat  -f-. 
Hence  mean  value  of  this  change  =  24,725  gram-units  -f  . 

B.  [20z  =  3O2]  =  59,200  units  of  heat  -f;  that  is  to  say 


the  separation  of  2  gram-molecules  of  ozone  (O3)  into  3  gram-  molecules 
of  oxygen  (O2)  is  attended  by  the  evolution  of  59,200  units  of  heat. 

1  For  thermal  details  concerning  the  action  of  metals  on  sulphuric  and  nitric 
acids  see  Naumann,  loc.  cit.  477—482. 

M.  C.  1  8 


2/4  CHEMICAL   STATICS.  [§  126 

The  comparative  thermal  instability  of  the  molecule  O3 
helps  us  to  understand  why  ozone  is  so  much  more  active  as 
an  oxidising  agent  than  ordinary  oxygen1. 

C.  If  Sa  represent  32  grams  of  octahedral  sulphur,  Sp  the  same  mass  of 
prismatic,  Sy  the  same  mass  of  soluble  amorphous,  and  Sa  the  same 
mass  of  insoluble  amorphous  sulphur  ;  then 

the  change  of  85  to  SY  is  accompanied  by  the  evolution  of 

So  units  of  heat ; 
Sy  to  Sa  „  „  absorption  of 

So  units  of  heat ; 

and      „  S0  to  Sa  „  „  evolution  of 

So  units  of  heat2. 

126.  Too  little  has  as  yet  been  done  to  allow  of  the 
application  of  thermal  measurements  to  the  classification  of 
the  elements  in  any  but  a  very  general  way. 

The  relations  existing  between  the  members  of  a  group  of 
elements  are  sometimes  summarised  in  the  thermal  values  of 
comparable  reactions  undergone  by  these  elements.  Thus, 
(see  table  p.  240)  taking  MendelejefTs  group  II.  we  have, 

Series 


468  3579        ii 

Ca      Sr      Ba  Mg     Zn      Cd       -        Hg 

atomic  weights    40      87     137  24       65      112  200. 

The  heats  of  formation  in  aqueous  solution  of  the  haloid 
salts  of  these  metals  are  arranged  in  the  following  table  (data 
from  Naumann's  book) : 

[M,  Cl2,  Aq]  [M,  Br2,  Aq]  [M,  I2,  Aq] 

Ca  187,600  165,800  I35>3oo 

Sr  195,700  173,800  143,400 

Ba  196,300  I74j4oo  144,000 

Mg  186,900  165,000  134,600 

Zn  112,800  90,900  60,500 

Cd  96,300  74,400  44,000 

Hg  59,900  ?  ? 

1  According  to  van  der  Meulen   (Ber.  16.  1853)  the  thermal   value  of  the 
change  in  question,  2O3=3O2,  is  about  68,000  units. 

2  For  more  details  see  Naumann,  he.  cit.  486. 


§  I2/]  APPLICATION    OF    PHYSICAL   METHODS.  2/5 

Hence  we  conclude  that  in  each  case  the  value  for 
Ba  >  Sr  >  Ca  >  Mg,  and  for  Mg  >  Zn  >  Cd  >  Hg.  In  other 
words,  the  thermal  value  of  the  change  [M,  X*,  Aq]  increases 
as  the  atomic  weight  of  M  increases,  when  M  is  a  member  of 
an  even  series  belonging  to  group  II.  but  decreases  as  the 
atomic  weight  of  M  increases,  when  M  is  a  member  of  an  odd 
series  of  the  same  group.  The  difference  between  the  values 
of  [M,  Xz,  Aq]  for  each  pair  of  elements  is  nearly  constant. 
Thus 

X=Cl  X^Er  X=l 

Ba  -  Sr  =      600  600  600 

Sr   -  Ca  =  8,100  8,000  8,100 

Ca  -  Mg=      700  800  700 

Mg-Zn  =74,100  74,ioo  74,ioo 

Zn  -  Cd  =  16,500  16,500  16,500 

Cd  -Hg  =  36,400  ?  ? 

The  close  relationship  of  magnesium  to  calcium,  and  also 
its  relations  to  barium  and  strontium,  and  the  comparatively 
feebly  marked  relations  existing  between  magnesium,  zinc, 
cadmium,  and  mercury,  are  brought  into  forcible  relief  by 
these  numbers1. 

127.  The  comparative  study  of  classes  of  compounds,  no 
less  than  that  of  classes  of  elements;  has  already  been  con- 
siderably advanced  by  the  application  of  thermal  methods. 
Thus  the  relations  between  the  oxides  and  oxyacids  of 
nitrogen,  phosphorus,  and  arsenic  are  suggested  by  the 
following  data 

[N2,  O3,  Aq]=  6,800  units  -  .  [P2,  O3,  Aq]  =  250,000  +  . 

[N',OVAq]  =  29,800     „      +  •  [P2,  0*,Aq]  =  405,5oo  +  . 

[N20'Aq,02]  =  36,600     „     +.  [PWAq,02]=  155,500  +  . 

[As2,  O3,  Aq]=i47,ioo  +  . 
[As2,  O6,  Aq]  =  225,400  +  . 
[As2O3Aq,  O2]=   78,300  +  . 

1  Attention  has  already  been  drawn  to  the  fact  that  there  exists  a  well-marked 
connection  of  a  periodic  character  between  the  atomic  weights  of  the  elements 
and  their  heats  of  combination  with  chlorine,  bromine,  and  iodine.  (See  antt, 
par.  109.) 

1 8— 2 


2/6  CHEMICAL   STATICS.  [§  I2/ 

The  superior  thermal  stability  of  the  oxides  of  arsenic  as 
compared  with  the  analogous  compounds  of  nitrogen,  and  the 
comparatively  very  great  stability  of  the  oxides  of  phos- 
phorus, are  rendered  evident  by  these  numbers.  A  compari- 
son of  the  heats  of  formation  of  nitric,  phosphoric  and  arsenic 
acids  (although  the  formula  of  the  first  is  not  strictly  com- 
parable with  that  of  the  second  and  third),  establishes  the  same 
point.  Thus 

[N,  O3,  H,  Aq]=49,ioo+  :  [P,  O*,  H3,  Aq]  =  3o5,3oo+  : 

[As,  O4,  H3,  Aq]  =  2i5,20o. 

If  the  heats  of  formation  of  the  three  oxyacids  of  phos- 
phorus are  compared,  it  is  seen  that  the  change  from  hypo- 
phosphorous,  or  phosphorous,  to  phosphoric  acid,  is  thermally 
very  probable, 

[P,  O4,  H3,  Aq]  =  3o5,30o  :  [P,  O3,  H3,  Aq]  =  227,6oo  : 

[P,  O*,  H3,Aq]=  1  39,800. 

A  comparison  of  the  thermal  changes  accompanying  the 
formation  and  decomposition  of  the  trichlorides  of  phosphorus, 
arsenic,  antimony,  and  bismuth  serves  to  illustrate  the  relations 
which  exist  between  analogous  chemical  changes,  and  gains  or 
losses  of  energy  by  the  changing  systems. 

[P,  Cl3]  =  75,3oo  :  [As,  Cl3]  =  7i,5oo  :  [Sb,  Cl3]  =  9i,4oo  :  [Bi,  Cl3]  =  9°,6oo. 
[PCI3,  Aq]  =  65,100;   giving  H8POS  +  3HC1. 
[Asd'.Aq]-  ,7,600;       „       As20,.3H20  +  6HCl 

1.  [SbOiAd-  7,700;       „       Sb20,3H,0+6HC. 

[Bid3,  Aq]=  7,800;  „  BiOCl.H2O  +  2HCl. 
In  the  decomposition  of  SbCl3  by  water,  the  greatest 
development  of  heat  (8,900  units)  corresponds  to  the  forma- 
tion of  the  oxychloride  Sb4O5Cl2  ;  the  further  change  of  this 
substance  to  Sb2O3  and  HC1  involves  absorption  of  a  little 
heat. 


Now  [BiOCl,  Aq]=  -  14,200,  if      *3  is  produced  . 

=  7,8oo-(-i4,20o)     .f  Bi2O3. 

! 


=  -  6,400  J  2 

were  produced. 


§  127]  APPLICATION   OF   PHYSICAL   METHODS.  277 

These  numbers  associate  the  stability  of  BiOCl  with 
great  loss  of  energy  in  the  formation  of  this  compound. 

Another  way  of  stating  the  thermal  reactions  of  analogous 
antimony  and  bismuth  hydroxides  illustrates  the  fact,  that 
while  antimony  hydroxides  are  acid  substances  the  correspond- 
ing bismuth  compounds  are  marked  by  basic  characters. 

Thus  |>SbO3H3,  HClAq]=  2,400;  (forming  Sb4O6Cl2)  : 

but  [BiO3H3,  HClAq]=i4,2oo;  (forming  BiOCl). 

The  complete  decomposition  of  a  haloid  salt  by  water  may 
produce  either  hydroxide,  hydrochloric  acid,  and  water  ;  or 
oxide,  hydrochloric  acid,  and  water.  Taking  the  latter  case, 
Thomsen  has  calculated  the  difference  between  the  heats  of 
formation,  in  presence  of  water,  of  oxides  and  chlorides,  and 
has  shewn  that  for  all  the  nonmetals,  except  tellurium,  anti- 
mony (trichloride),  and  bismuth,  this  difference  is  positive. 
We  are  "not  concerned  here  with  tellurium  ;  for  antimony  and 
bismuth  the  differences  are 

(  [Sb2,  O3,  H20]  -  [Sb,  C13]=  7,680  units  -  . 
03,  H20]-[Bi,Cl3]  =  2i,7oo    „    -. 


Hence  we  should  conclude  that  SbCl3  and  BiCl3  would  differ 
from  other  analogous  chlorides  in  being  only  partially  decom- 
posed by  water,  and  that  the  decomposition  would  be  carried 
further  in  the  case  of  antimony  than  in  that  of  bismuth. 
This  expectation  is  confirmed  by  the  actually  occurring  re- 
actions1 ;  in  the  case  of  SbCl3,  fths  of  the  total  decomposition 
(i.  e.  decomposition  into  oxide,  hydrochloric  acid,  and  water) 
is  accomplished  by  the  formation  of  Sb4O6Cl2  ;  in  the  case  of 
BiCl3,  the  formation  of  BiOCl.  H2O  represents  frds  of  the 
total  decomposition. 

A  comparative  study  of  some  of  the  thermal  relations  of 
the  hydracids  and  oxyacids  of  the  halogens  helps  towards 
a  classification  of  the  latter  group  of  acids2. 

1  For    more    details    see    Thomsen,     Thermochemische    Untersuchungen,    2. 
2  5—  395  298—  3°4;  and  364—  374. 

2  See  Thomsen,  loc.   cit.  1.   150  —  155,   and    240  —  253;    also  Jahn,  loc.  tit. 
136—138. 


2/8  CHEMICAL   STATICS.  [§  12? 

The  close  thermal  analogy  between  the  hydracids  in 
question  is  exhibited  by  these,  among  other,  numbers  ; 

[HX,  Aq]  [H^Aq,  NaOHAq] 
X=Cl  =  17,400  X=  01  =  13,700 

X=Er  =  19,900  Jf=Br=i3,7oo 

X=l    =19,200.  X=l    =13,700. 

But  when  we  compare  the  heats  of  formation  of  these  acids, 
in  aqueous  solutions,  we  find  that  the  value  of  this  constant 
for  each  acid  decreases  as  the  atomic  weight  of  the  halogen 
increases  :  thus 

[H,  X,  Aq] 

x=a=  39,300 

X=Er  =28,400 
X=l    =13,200. 

The  three  oxyacids  corresponding,  in  composition,  to  the 
three  hydracids,  are  HC1O3,  HBrO3,  and  HIO3.  The  following 
numbers  shew  that,  in  some  respects  at  any  rate,  the*  thermal 
relations  between  HC1O3  and  HBrO3  are  analogous  to  those 
between  HC1  and  HBr:— 

[H,  X,  O3,  Aq] 
X=Cl  =  23,900 


hence  the  difference,  [H,  Cl,  Aq]  -  [H,  Br,  Aq],  is  approximately  equal 
to  the  difference  [H,  Cl,  O3,  Aq]  -  [H,  Br,  O3,  Aq]. 

From  this  we  might  provisionally  conclude  that  the  differ- 

ence between  the  heats  of  formation,  in  aqueous  solutions, 

of  chloric  and  iodic  acids,  would   probably   be   nearly   the 

same  as  the  difference  between  the  heats  of  formation,  under 

the  same  conditions,  of  hydrochloric  and  hydriodic  acids.   The 

value   of  the   second   difference   is   26,100;    hence,   on   this 

supposition,  the  first  difference  should  be  about  26,000.    Now, 

[H,C1,  03,  Aq]  =  23,900; 

/.  [H.I,  03,Aq]=-  2,100. 

But  experiment  shews  that 

[H,  I,  03,Aq]=+  55,700. 

Hence  it  is  evident  that  iodic   acid  differs  in  the  most 
marked  manner  from  bromic  and  chloric  acids.    This  difference 


§  128]  APPLICATION   OF   PHYSICAL   METHODS.  279 

is  accentuated  in  the  numbers  expressing  the  heats  of  forma- 
tion of  these  three  acids  from  the  three  hydracids :  thus, 

[H^Aq,  O3] 
^=0  =  15,400-. 
Jf=Br=i5,9oo-. 
X=l    =42,600  +  . 

lodic  acid  is  probably  dibasic,  and  may  be  represented  by 
the  formula  H^O/. 

128.  A  comparison  of  the  mutual  thermal  actions  of  acids 
and  bases  throws  considerable  light  on  the  classification  of  the 
substances  which  are  included  under  these  terms.  The  first 
volume  of  Thomsen's  Untersuchungen  is  devoted  to  a  con- 
sideration of  this  subject. 

'  Heat  of  neutralisation  of  an  acid  by  a  base'  is  defined  as, 
the  quantity  of  heat  evolved  on  mixing  equivalent  quantities, 
in  grams,  of  the  acid  and  base,  in  dilute  aqueous  solutions, 
the  products  of  the  action  being  also  soluble  in  water. 

Thomsen  employs  a  solution  of  2NaOH  in  about  200  H2O 
(grams),  and  adds  the  acid  solution  diluted  to  a  similar  degree, 
temperature  being  18° — 19°;  in  other  words  he  determines  the 
thermal  value  of  the  change 

[2NaOHAq,  2H^TAq]  in  the  case  of  a  monobasic  acid, 
[2NaOHAq,  HaATAq]  „  dibasic  „ 

|>NaOHAq,  |H3^Aq]  „  tribasic  „ 

ONaOHAq,  £H4JfAq]  „  tetrabasic      „ 

(X=acid  radicle) 

Most  of  the  general  conclusions  drawn  by  Thomsen,  and 
others,  belong  more  to  chemical  kinetics  than  to  statics,  but 
some  of  the  generalisations  may  fitly  be  introduced  here8. 

The  commoner  acids  may  be  broadly  divided  into  four 
groups  according  to  the  values  of  their  heats  of  neutralisation, 
as  thus  defined. 

I.  Those  acids  which  have  a  heat  of  neutralisation 
approximately  equal  to  20,000  gram-units  : — 

HNO2,     HC1O,     H2B2O4,     H2CO3    &c. 

1  See  Thomsen,  Ber.  1.  112  (or  Untersuchungen,  2.  423). 

2  See  especially  for  more  details  Thomsen, /for.  fit.  1.  293 — 309,  and  422 — 449. 


28O  CHEMICAL  STATICS.  [§  128 

II.  Those    acids    which   have   a  heat   of  neutralisation 
approximately  equal  to  25,000  gram-units  : — 

H2Cr04,     C2H4(C02H)2,     CH2CHOH(CO2H)2    &c. 

III.  Acids  the  heat  of  neutralisation  of  which  is  equal 
to  about  27,000  gram-units : — 

HC1,     HBr,     HI,    HC1O3,     HBrO3,     HIO3,     HNO3,     H2S2O3, 
H2SiF6,     H.CO2H,     CH3.CO2H     &c. 

Most  of  the  acids  belong  to  this  class. 

IV.  Acids  having  a  heat  of  neutralisation  greater  than 
27,000  units,  and  varying  from  28,000  to  32,500  units : — 

CH2C1.CO2H,    CHC12.CO2H,    CC13.CO2H,    H2C2O4,    H3PO3,    H2SO3, 
HaS04,    H2Se04,    HF,    HPO3    &c. 

A  few  acids  have  heats  of  neutralisation  less  than  20,000  units. 

The  value  of  the  heat  of  neutralisation  of  an  acid  does  not 
appear  to  depend  on  the  basicity,  nor  on  the  composition  of 
the  acid ;  neither  does  it  depend  on  what  Thomsen  calls  the 
'  avidity '  of  the  acid,  i.e.  the  striving  of  the  acid  to  displace 
another  from  combination  with  a  base.  The  relative  'avidities' 
of  acids  will  be  considered  in  book  II1.,  meanwhile  the 
meaning  of  the  term  may  be  made  clear  by  an  example. 
When  equivalent  quantities  of  NaOH,  HNO3,  and  H2SO4,  are 
mixed  in  dilute  aqueous  solutions,  two-thirds  of  the  NaOH 
are  found  to  combine  with  the  HNO3,  and  one-third  with  the 
H2SO4.  Hence  HNO3  is  said  to  have  an  '  avidity'  for  NaOH 
twice  as  great  as  that  of  H2SO4  for  the  same  base;  HNO3  in 
aqueous  solution  is  therefore  a  '  stronger'  acid  than  H2SO4. 

The  basicity  of  an  acid  may  be  determined  by  thermal 
methods.  One  gram-molecule  of  the  acid  in  dilute  aqueous 
solution  is  mixed  with  J,  -J-,  J,  I,  2,  &c.  gram-molecules  of 
NaOH  also  in  dilute  solution,  and  the  heat  evolved  in  the 
reactions  is  measured.  (The  ordinary  formulae  NaOH,  H2SO4, 
&c.  are  here  assumed,  for  the  sake  of  convenience  of  nomen- 
clature, to  be  molecular).  Comparing  in  this  way  HC1, 
H2SO4,  and  CgHHO7  (citric  acid),  we  have  this  result, 

1  Chap.  III.  par.  233. 


§  128]  APPLICATION   OF   PHYSICAL   METHODS.  28  1 

[HClAq,  £NaOHAq]  =  about  6,000  [H2SO4Aq,£NaOHAq]  =  about  7,000 
[HClAq,    NaOHAq]  =  13,500  [H2SO4Aq,    NaOHAq]=  14,500 

[HClAq,  2NaOHAq]=  13,500  [H2SO4Aq,  2NaOHAq]=          31,000 

[H2SO4Aq,  3NaOHAq]  =          31,000 

[C6H8O7Aq,  NaOHAq]=i2,4oo 
[C6H8O7Aq,  2NaOHAq]  =  24,800 
[C6H807Aq,  3NaOHAq]  =  38,000 
[C6H8O7Aq,  4NaOHAq]  =  38,000. 

Hence  we  conclude  that  HC1  is  a  monobasic,  H2SO4  a 
dibasic,  and  C6H8O7  a  tribasic  acid. 

The  application  of  this  method  to  the  oxyacids  of  phos- 
phorus and  arsenic  leads  to  interesting  results1. 

The  data  are  presented  in  the  following  table  :  — 

[H3P03Aq,  .NaOHAq] 

Difference. 


[H3PO2Aq,  .NaOHAq]  x=\=  7,400 

.=  1  =  14,800 
.=  2  =  28,500 
.=  3  =  28,900. 


.=  1  =  15,000       .  .=  1  =  14,800  7'4CX 

.=2  =  15,000.  .=  2  =  28,500  !3*7oc 


[HPO3Aq, 
x=  i  =  14,400. 
^•=2=14,800  (about). 

The  heat   of  neutralisation  of  this   acid  gradually  increases  till  it 
becomes  equal  to  about  33,600  units. 

[H3PO4Aq,  *NaOHAq]  [H4P2O7Aq,  ^NaOHAq] 

Difference.  Difference. 

x=\=  7>4oo  ^-=1  =  14,400 

^-=1  =  14,800        7,400  ^=2  =  28,600       'I4'20C 

12,300  24,100 

.=  2  =  27,IOO         6  ^=4=52,700          * 

.=3  =  34,000         y  .=  6  =  54,500. 

*=6  =  35,3oo.      !'3<X 

[H3As03Aq,  .NaOHAq]  [H3AsO4Aq,  .NaOHAq] 

Difference.  Difference. 

.=  1=    7,300  *=£=    7,400  , 

.=  2  =  13,800     6'5°°  .=  1  =  15,000       7'f° 

1,200  I2,600 

.=  4=15,000  .=  2  =  27,600 

600.  8,400 

.  =  6=15,600.  .=  3  =  36,000    ^ 

.=6  =  37,400. 

1  See  Thomsen,  loc.  cit.  1.  201  —  205  ;  and  Jahn,  Die  Grundsatze  der  Thermo- 
chemie,  no  —  113. 


282  CHEMICAL  STATICS.  [§  128 

Hypophosphorous  (H3PO2),  and  metaphosphoric  (HPO3) 
acids  are  evidently  monobasic ;    phosphorous   (H3PO3),    and 
arsenious  (H3AsO8)   acids  are  dibasic ;   orthophosphoric,  and 
arsenic  acids  (H3PO4  and  H3AsO4)  are  tribasic,  and  pyrophos- 
phoric  acid  (H4P2O7)  is  tetrabasic.     The  gradual  rise  in  the 
value  of  the  heat  of  neutralisation  of  HPO3Aq  is  explained  by 
the  fact,  that  an  aqueous  solution  of  this  acid  is  slowly  decom- 
posed with  formation  of  H3PO4;  the  final  number  obtained 
(33,600)  therefore  represents  the  neutralisation  of  H3PO4,  and 
not  of  HPO3.     A  comparison  of  the  heats  of  neutralisation  of 
H3PO3  and  H3AsO3  shews  that  the  former  is  a  much  'stronger' 
acid  than  the  latter.     A  similar  comparison  of  H3PO4  with 
H3AsO4  however  shews  that  these  acids  are  very  analogous. 
Thus,  the  heat  of  neutralisation  of  H3PO4  =  34,000,  and   of 
H3AsO4  =  36,000  ;  moreover  about  three-fourths  of  the  total 
heat  is  evolved,  in  each  case,  during  the  replacement  of  the 
first  and  second  atom  of  hydrogen  by  sodium ;    and  finally 
the   addition    of  an    excess    of  soda  over  that  required   for 
neutralisation,  causes  the  evolution  of  an  appreciable  quantity 
of  heat.      The   last   fact   is  explained    by    the   comparative 
instability  in    aqueous   solutions   of  Na3PO4    and    Na3AsO4, 
which  salts  are  partially  separated  by  water  into  Na2HPO4  and 
H3PO4,  and  Na2H AsO4  and  H3AsO4,  respectively ;  hence  the 
addition  of  more  soda  than  is  required  to  form  either  of  these 
salts  evolves  a  little  heat,  because  it  enters  into  reaction  with 
the  small  quantity  of  phosphoric,  or  arsenic  acid,  present  in  the 
liquid.     A  similar  phenomenon  is  noticed   in  the  neutralisa- 
tion of  tetrabasic  phosphoric  acid  ;  more  than  one-fourth  of 
the  total  quantity  of  heat  is  evolved  during  the  action  of  the 
first  molecule  of  NaOH,  and  more  than  a  half  during  the  action 
of  the  first  and  second  molecules.     We  should  thence  expect 
the  tetrasodic  salt  to  be  less  stable  than  the  disodic  salt ;  that 
this  is  so  is  shewn  by  the  evolution  of  1800  units  of  heat  on 
addition    of   two   molecules  of  soda  more  than  the  amount 
required  for  complete  neutralisation1. 

The  polybasic  acids  may  also  be  classified  in  accordance 

1  In  these,  and  other  similar  reactions,  for  convenience  of  nomenclature,  the 
formulae  NaOH,  H2SO4,  £c.  are  regarded  as  molecular. 


§  128]  APPLICATION   OF   PHYSICAL   METHODS.  283 

with  the  thermal  value  of  the  action  of  each  gram-molecule 
of  soda  on  one  gram-molecule  of  acid.  Thus,  comparing 
oxalic  with  sulphurous  acid,  we  find  the  difference  between 
the  quantities  of  heat  evolved  during  the  action  of  the  first 
and  second  molecules  of  soda,  in  the  case  of  oxalic  acid  to 
be  600,  and  in  that  of  sulphurous  acid  to  be  2750 :  the  data 
are, 

Difference. 

[H2C2O4Aq,    NaOHAq]=i3,840\  x[H2SO3Aq,    NaOHAq]=  15,850 

[H2C204Aq,  2NaOHAq]=i4,44ox  \[H2SO3Aq,  2NaOHAq]=  13,100. 

Thomsen1  divides  the  dibasic  acids  which  he  has  examined 
into  three  groups  : — 

I.  Those  in  the  neutralisation  of  which  each  molecule 
of  soda  has  the  same  thermal  value :  this  group  is  at  present 
represented  by  H2SiF6,  and  H2PtCl62. 

II.  Those  in  the  neutralisation  of  which  the  first  mole- 
cule   of  soda  has  a  smaller  thermal  value  than  the  second, 
the  difference  between  the  two  values  varying  from  450  to 
1900  units:    this  group  contains  the  acids   H2SO4,   H2SeO4, 
H2C204  and  H2.C4H4O6. 

III.  Those  in  the  neutralisation  of  which  the  first  mole- 
cule of  soda  has  a  larger  thermal  value  than  the  second,  the 
difference  between  the  two  values  varying  from  1850  to  2750 
units :  the  acids  in  this  group  are  H2SO3,  H2SeO3,  H2CO3  and 
H2B2O4;  H2CrO4,  H2PHO3,  and  C2H4(CO2H)2  also  probably 
belong   to  this  group,  although  the  differences  between  the 
thermal  values  of  the  first  and  second  molecule  of  soda  are 
smaller   in   the   case   of  these   acids   than  of  those  already 
mentioned  (see  below). 

Data  on  which  the  foregoing  classification  is  based. 
GROUP  I. 

Heat  evolved  in  action  of  TT  c*TT  TJT  rurM  2 

NaOH  H2bll<6  HjjPtCV 

i st  molecule  ...  ...  13, 300  13,600 

2nd         „  ...  ...  13,300  13,600. 


1  loc.  cit.  1.  302 — 306. 

3  But  it  seems  doubtful  whether  the  numbers  obtained  by  Thomsen  really 
represent  the  neutralisation  of  this  acid.  See  Thermochemische  Untersuckttngen, 
I.  229. 


284 


CHEMICAL   STATICS. 


[§128 


GROUP  II. 

Heat  evolved  in  action  of 
NaOH. 

H2S04 

H2Se04 

H2C204 

H2.C4H406 

i  st  molecule 
2nd         „ 

14,750 
16,650 

14,750 
15,650 

13,850 
14,450 

12,450 
12,850. 

ISt 

2nd 


ist 
2nd 


GROUP  III. 
H2SO3  H2SeO3 
15,850  14,750 
13,100  12,250 


H2C03        H2B204 

11,000  11,100 

9,150        8,900. 


H2Cr04 

13,150 

11,550 


H2PHO3 
14,850 
13,600 


C2H4(C02H)2 
12,400 
11,750. 


The  reaction  between  an  acid  and  its  normal  salt  is  accom- 
panied by  absorption  of  heat  when  the  acid  belongs  to  Group 
II,  and  by  evolution  of  heat  when  it  belongs  to  Group  III1. 
The  tribasic  acids  examined  by  Thomsen  are  divisible  into 
two  groups,  corresponding  to  the  second  and  third  groups  of 
the  dibasic  acids  :  thus, 


GROUP  II. 


H,C5H30 

(Acomc  acid) 

H8.C6H80T 

(Citric  acid) 

... 

12,850 

12,650 

12,950 

I2,8OO 

13,350 

13,550. 

GROUP  III. 

H3AsO4 

H3P04 

... 

15,000 

14,850 

... 

12,600 

12,250 

... 

8,350 

6,950. 

Heat  evolved  in  action  of 
NaOH 

ist  molecule 

2nd 

3rd 


ISt  „ 

2nd        „ 
3rd         „ 

Thomsen  suggests  (l.  pp.  304-5)  that  the  foregoing  classi- 
fication of  dibasic  and  tribasic  acids  may  be  summarised  in 
these  typical  formulae : — 

1  Hydrofluoric  acid  acts  on  potassium  fluoride  with  absorption  of  370  gram- 
units  of  heat ;  it  would  appear  to  belong  to  Thomsen's  second  group.  (See  Guntz 
Compt.  rend.  97.  256.) 


§  128]  APPLICATION    OF    PHYSICAL   METHODS.  285 

Dibasic  Acids. 
Acid  of  Group  I.        Typical  formula  RH2  e.g.  SiF6.H2 ; 

II-  „  R(OH)2     e.g.  S02.(OH)2; 

III.  „  R(OH)H  e.g.  S02(OH).H. 

Tr i basic  Acids. 

Acid  of  Group  II.      Typical  formula  R(OH)3     e.g.  C4H6O4(OH)3  ; 
III.  „  HR(OH)H  e.g.  HPO3.(OH).H. 

The  'heat  of  neutralisation  of  a  base'  is  defined  by 
Thomsen1  as  the  thermal  value  of  the  change  which  occurs 
when  equivalent  quantities  of  base  and  acid  react  in  dilute 
aqueous  solution,  the  products  of  the  action  being  also  soluble 
in  water.  A  dilute  solution  of  one  gram-molecule  of  sulphuric 
acid  (i.e.  the  amount  of  acid,  in  grams,  expressed  by  the 
formula  H2SO4)  is  employed  ;  temperature  being  18° — 19°. 

In  other  words,  Thomsen  measures  the  thermal  values  of 
the  following  reactions  : — 

[H2SO4Aq,  2MOHAq      or  2NAT3Aq]  in  the  case  of  a  monacid  base, 
[H2SO4Aq,  M(OH)2Aq    or    N2AT6Aq]  „  diacid     „ 

[H2SO4Aq,  |M(OH)3AqorfN3Ar9Aq]  „  triacid    „ 

[H2SO4Aq,|M(OH)4Aqor£NMr12Aq]  „  tetracid     „ 

(X=H,  or  a  radicle  C«H2M  +  1) 

The  bases  which  are  soluble  in  water  may  be  divided  into 
two  thermal  groups  : — 

I.  The  group  of  the  hydrates  or  hydroxides,  represented 
by  NaOH  and  KOH. 

II.  The  group  of  the  anhydrous  bases,  represented  by 
NH3. 

The  first  group  comprises  LiOH,  NaOH,  KOH,  and 
T10H;  Ca(OH)2,  Sr(OH)2,  and  Ba(OH)2;  N(CH3)4OH, 
(C2H5)3S.OH,  and  Pt  (NH3)4(OH)2:  the  mean  value  of  the 
change  [H2SO4Aq,  2MOHAq  (or  M(OH)2Aq)]  is  equal  to 
31,350  units +  ,  when  M(OH)  or  M(OH)2  is  one  of  the  bases 
of  this  group. 

The  second  group  comprises  NH3  and  the  amines  of  the 
form  NH2(CnH2n+1)  and  NH(CnH2rt+1)2:  the  mean  value  of 

1  See  especially  loc.  cit.  1.  422 — 449. 


286  CHEMICAL   STATICS.  [§  128 

the    change    [H2SO4Aq,    2iVX3Aq]    is    equal    to    28,200+, 
when  NX*  is  one  of  the  bases  of  this  group. 

Substitution  of  negative  radicles  for  H  in  NH3  causes  a 
considerable  decrease  in  the  heat  of  neutralisation  of  the  base  ; 
thus, 

[2NH2(C6H5)Aq,  H2SO4Aq]=  15,500, 
and  |>NH2(C7H7)Aq,  H2SO4Aq]=  15,200  ; 
also  [2NH2OHAq,  H2SO4Aq]  =21,600. 

When  CO  is  substituted  for  H  in  2NH3,  the  heat  of 
neutralisation  of  the  product,  [(NH2)2CO]  is  almost  nil. 

Measurements  of  the  quantities  of  heat  evolved  during  the 
action  of  acids  on  those  bases  which  are  insoluble  in  water 
shew  great  irregularities.  The  true  heats  of  neutralisation 
of  these  bases  cannot  be  determined.  But  from  the  analogies 
between  the  hydrates  of  barium,  strontium,  and  calcium,  and 
those  of  magnesium,  zinc,  and  manganese1,  Thomsen  concludes 
that  the  heats  of  neutralisation  of  the  bases  of  the  magnesian 
class  are  equal  to  those  of  the  bases  of  the  alkaline  earth 
metals  ;  but  as  the  heats  of  neutralisation  of  the  latter  and  of 
the  alkalis  are  equal,  Thomsen  argues  that  the  mean  value  of 
the  heat  of  neutralisation  of  M(OH)2,  when  M  =  Mg,  Mn,  Ni, 
Co,  Fe,  Cd,  Zn,  or  Cu,  is  31,350  units. 

From  what  has  been  said  regarding  the  classification  of 
acids  in  accordance  with  their  heats  of  neutralisation2,  it 
will  be  apparent  that  if  2HClAq  is  substituted  for  H2SO4Aq 
in  the  preceding  reactions,  the  mean  heats  of  neutralisation  of 
the  two  groups  of  bases  will  be  represented  by  numbers 
smaller  than  31,350  and  28,200  respectively. 

The  identity  of  the  numbers  expressing  the  heats  of 
neutralisation  of  bases  of  such  different  composition  as  KOH 
and  Pt(NH3)4(OH)2  points  to  the  possibility  of  connecting 
similar  changes  of  energy  with  similarity  of  chemical  type, 
maintained  through  series  of  more  or  less  unlike  individuals. 
The  heats  of  neutralisation  of  the  bases  MXS  also  point 
to  the  existence  of  a  relation  between  change  of  energy  and 

1  See  Thomsen,  loc.  cit.  1.  435 — 440. 

2  See  anfe,  p.  280. 


§§128,129]     APPLICATION    OF    PHYSICAL   METHODS.  287 

composition  ;  but  the  influence  of  the  structure  of  the  indi- 
vidual substance  is  shewn  in  the  small  values  obtained  for 
NH2(C6H5)  and  NH2(C7H7),  in  which,  although  the  chemical 
type  is  maintained,  the  typical  thermal  value  is  widely  de- 
parted from. 

The  quantity  of  heat  evolved  in  the  reaction  [2MOHAq,' 
H X Aq]  when  M  =  K,  Na,  &c.  is  nearly  constant,  whether 
X  =  C\,  Br,  or  I;  but  the  value  of  the  reaction  [PbO.H2O, 
H^TAq],  or  [T12O.H2O,  H^Aq]  &c.  differs  very  considerably 
according  as  X  =  Cl,  Br,  or  I.  In  the  reaction  with  PbO.H2O, 
the  thermal  value  is  greatest  for  HIAq,  and  least  for  HClAq. 
Now  in  the  reactions  just  mentioned,  haloid  salts  are  produced 
which  are  only  slightly  soluble  :  if  the  heats  of  solution  of 
these  salts  are  added  to  the  values  of  the  apparent  heats  of 
neutralisation  of  the  bases,  it  is  found  that  the  true  heats  of 
neutralisation  of  PbO.H2O,  T12O.H2O  &c.  are  represented  by 
the  same  number,  whether  HClAq,  HBrAq,  or  HIAq  is  the 
acid  employed.  If  it  is  granted  that  the  true  heats  of 
neutralisation  of  these  acids  are  the  same  for  other  bases 
which  form  insoluble  haloid  salts,  it  becomes  possible  to 
calculate  the  heats  of  solution  of  these  salts.  Thomsen 
has  done  this  for  PbCl2,  PbBr2,  PbI2,  AgCl  &c.  and,  carrying 
out  the  same  method,  he  has  even  given  a  value  for  the  heat 
of  solution  of  barium  sulphate. 

Thomsen's  investigation  of  the  heats  of  neutralisation  of 
acids  and  bases  serves  to  shew  the  complexity  of  many  of 
the  reactions  to  which  thermal  values  are  assigned,  and  also 
the  necessity  of  making  all  the  conditions  of  the  changes  we 
wish  to  study  as  exactly  comparable  as  possible.  At  the 
same  time  it  illustrates  one  of  the  dangers  which  beset  the 
employment  of  thermal  methods  in  chemistry,  the  danger 
namely  of  theorising  regarding  chemical  changes  which  do  not 
occur,  and  of  speculating  about  chemical  compounds  which 
have  no  existence. 

129.  The  primary  aim  of  thermal  chemistry  was  stated 
in  par.  117  to  be  the  measurement  of  the  differences  between 
the  quantities  of  energy  possessed  by  chemical  systems  when 
in  certain  definite  initial  and  final  states ;  the  basis  of  these 


288  CHEMICAL   STATICS.  [§  1 29 

measurements  being,  the  deduction  from  the  general  theory 
of  energy,  which  states,  that  the  total  loss  of  energy  during 
the  passage  of  a  chemical  system  from  a  definite  initial  to  a 
definite  final  state  is  independent  of  the  intermediate  states. 

The  application  of  this  generalisation  was  illustrated  in 
par.  1 20.  We  are  now  however  in  a  position  more  fully 
to  discuss  the  relations  existing  between  gain  or  loss  of 
heat,  and  gain  or  loss  of  energy  by  a  chemical  system.  It 
will  be  advantageous  to  confine  our  consideration  at  pre- 
sent to  gaseous  substances.  When  heat  is  imparted  to  a 
gaseous  system  of  chemical  substances,  a  portion  may  be 
employed  in  increasing  the  kinetic  energy  of  motion  of  the 
molecules,  i.e.  in  raising  the  temperature,  of  the  system; 
another  portion  may  be  employed  in  doing  work  against 
external  forces,  e.g.  in  causing  expansion  of  the  system  ;  and 
another  portion  may  do  work  against  molecular  and  atomic 
forces,  and  so  produce  a  rearrangement  of  molecules,  or 
atoms,  i.e.  may  cause  chemical  changes  to  proceed  within  the 
system.  The  exact  manner  of  the  distribution  of  the  energy 
imparted  in  the  form  of  heat  will  vary  in  each  special  case. 
It  is  evident  that  the  thermal  value  of  the  purely  chemical 
part  of  a  change — say  of  the  system  2H2  +  O2  to  the  system 
2H2O — will  vary  according  to  variations  in  the  physical  con- 
ditions under  which  the  change  proceeds,  and  more  especially 
according  to  variations  of  temperature. 

The  difference  between  the  energy  of  the  system  2H2+  O2 
and  that  of  the  system  2H2O  (both  in  grams)  at  ordinary 
temperatures,  say  at  15°,  is  measured  by  136,800  thermal 
units ;  what  will  be  the  value  of  the  difference  between  the 
same  systems  at  200°  ?\ 

Let  <215  and  Qm  represent  the  two  differences  :  let  £7=  the 
quantity  of  heat  which  must  be  imparted  to  the  first  system 
(2H2-}-O2)  in  order  to  raise  its  temperature  from  15°  to  200°; 
let  F=the  quantity  of  heat  which  must  be  imparted  to  the 
second  system  (2H2O)  to  raise  its  temperature  through  the 
same  interval ;  then 

Q*»=Qu+V-K 

1  See  Naumann,  loc.  cit.  212,  213. 


§  129]  APPLICATION   OF   PHYSICAL   METHODS.  289 

To  find  U,  we  have  the  following  data  : 

Specific  heat  of  hydrogen  (referred  to  an  equal  weight  of  water)  =  3*409. 
„  oxygen  „  „  =0-2175. 

200°-  15°=  185°. 

.*.  4. 185  .  3*409  =2522  thermal  units  needed  for  the  hydrogen  of  the 

first  system  ; 
and  32.185.0*2175  =  1288  thermal  units  needed  for  the  oxygen  of  the 

first  system  ; 
.'.  £7=3810  thermal  units. 

To  find  V  we  have  the  data : 

Specific  heat  of  water  =i  ;  heat  of  vaporisation  of  water =5  36*5. 
Spec,  heat  of  water  gas  =  0*4805  (up  to  temperature  somewhat  near  200°). 
.'.  for  raising  temperature  of  system  2H2O  from  15°  to  100°,  are  required, 

36.85.1  =  3060  thermal  units  ; 

for  changing  2H2O,  liquid,  at  100°  into  2H2O,  gaseous,  at  100°,  are  re- 
quired, 36.  536*5  =  19314  thermal  units  ; 

for  raising  temperature   of   2H2O,  gaseous,  from  100°  to  200°,  are 
required,  36 .  100 .  0*4805  =  1730  thermal  units  ; 

.*.   F=24,io4  thermal  units. 
And        .*.   (2200=136,800  +  3810-24,104=116,506  thermal  units. 

The  difference  between  the  energies  of  the  systems, 
2H2  +  O2,  and  2H2O  (in  grams)  at  15°  is  measured  by  136,800 
thermal  units;  whereas  the  difference  between  the  energies 
of  the  same  systems  at  200°  is  measured  by  1 16,506  thermal 
units.  Or  we  may  say  [>H2,  O2]  at  I5°-[2H2,O2]  at  200° 
=  20,294  units. 

We  have  assumed  that  the  total  loss  of  energy  during  the 
chemical  change  is  measured  by  the  quantity  of  heat  evolved. 

Thomsen  has  considered  the  influence  of  temperature- 
changes  on  the  thermal  values  of  the  chemical  reactions  be- 
tween liquids1. 

Let  the  action  which  is  to  be  investigated  occur  between 
two  liquids  :  let  A  be  the  number  of  gram-molecules  of  the 
first,  and  B  the  number  of  gram-molecules  of  the  second 
liquid  (using  'molecule'  as  =  amount  expressed  by  formula), 
and  let  a  =  specific  heat  of  the  first,  and  ft  —  specific  heat  of 

1  See  especially  loc.  cit.  1.  65 — 70. 
M.  C.  19 


2QO  CHEMICAL   STATICS.  [§  1  29 

the  second  liquid  ;  further  let  7  =  specific  heat  of  the  liquid  ob- 
tained by  mixing^  and.Z?;  then  the  calorimetric  equivalents  of 
the  three  liquids  are  (i)  A.z  =  qat  (2)  R/3  =  qb}  (3)  (A  +  B).  7  =  qc. 
For  small  variations  of  temperature  the  values  of  the 
specific  heats,  and  therefore  of  the  calorimetric  equivalents,  may 
be  regarded  as  independent  of  temperature.  Then  putting 
RT  as  the  thermal  value  of  the  change  represented  by  [A,B] 
at  temperature  T,  and  Rt  as  the  value  of  the  same  change 
of  temperature  t  we  get  * 


And  from  this,  the  variation  in  the  value  of  R  for  each  degree 
of  temperature  may  be  found,  by  the  equation 


This  formula  is  applied  by  Thomsen  to  the  reactions  be- 
tween acids  and  bases  at  varying  temperatures2. 

To  obtain  a  perfectly  general  formula  it  would  however  be 
necessary  to  study  the  relation  between  the  specific  heat  and 
the  temperature  of  each  solution  employed,  and  also  of  the 
solution  produced  by  the  chemical  change  :  it  would  also  be 
necessary  to  know  the  relation  between  the  variation  in  the 
value  of  the  calorimetric  equivalent  of  each,  solution  and  the 
composition  of  that  solution,  i.e.  the  relative  number  of  gram- 
molecules  of  salt  and  water  contained  therein3.  Thomsen's 
general  conclusion4  —  based  on  the  examination  of  the  in- 
fluence of  water  of  dilution  on  H2SO4Aq,  HClAq,  NaOHAq, 
Na2SO4Aq,  NaClAq,  Na2SO42HClAq,  and  H2SO42NaClAq 
—  is,  that  the  calorimetric  equivalent  of  a  solution  mixed  with 
water  is  always  less  than  the  sum  of  the  calorimetric  equiva- 
lents of  the  original  solution  and  the  added  water  :  i.e. 

qc<a  +   b    and  .'.  3>=  --= 


1  See  for  details  shewing  how  these  formulae  are  obtained,  Thomsen,  loc.  cit. 
66—67. 

2  loc.  cit.  1.  68—70. 

3  Tabulated  data  bearing  on  both  of  these  points  will  be  found  in  Naumann, 
loc.  cit.  pp.  289  —  310. 

4  loc.  cit.  1.  80—88. 


§  129]  APPLICATION    OF   PHYSICAL   METHODS.  2QI 

E.  Wiedemann  has  recently  investigated  the  connection 
between  the  calorimetric  equivalents  of  certain  solutions  and 
the  relative  quantities  of  salt  and  water  contained  therein1. 

The  calorimetric  equivalent  of  a  solution  of  a  salt  with 
molecular-weight,  or  rather  formula-weight,  M,  dissolved 
in  n  molecules  of  solvent  having  molecular  weight  m,  is 
evidently2  c  (M  +  nm),  when  c  —  specific  heat  of  the  solution. 
Wiedemann  finds  that  in  the  cases  of  aqueous  solutions  of 
sodium  chloride,  sulphate,  and  nitrate,  and  ammonium  sul- 
phate, the  calorimetric  equivalent  (or  it  may  be  called  the 
molecular  heat,  using  the  term  'molecular'  as  already  defined) 
of  very  concentrated  solutions  is  greater  than  that  of  the 
water  contained  therein  ;  as  the  solutions  are  diluted,  a  point 
is  reached  at  which  the  calorimetric  equivalents  of  the  solution 
and  of  the  water  therein  become  equal  ;  and  lastly  the  calori- 
metric equivalent  of  still  more  dilute  solutions  is  less  than 
that  of  the  water  alone.  In  other  words,  if  the  calorimetric 
equivalent  of  the  water  in  the  solution  is  18  »,  then 


for  concentrated  solutions  c(TA  +  nm}>  i8n\  for  aqueous    solutions 

for  solutions  of  mean  concentration  c  (M  +  nm}  =  i8«>   of    NaCl,      Na2SO4, 
for  dilute  solutions  c  (M  +  »/«)<  i8«)    NaNO 


Wiedemann's  results  seem  to  give  a  general  confirmation  to 
those  of  Thomsen3. 

The  relations  between  the  calorimetric  equivalents,  and 
therefore  the  relations  between  the  thermal  changes  and  the 
temperature,  of  solutions  of  hydrated  and  dehydrated  salts 
are  more  complicated  than  those  already  considered.  Thus, 
solutions  made  by  dissolving  (i)  one  gram-molecule  of  MgSO4 
in  100  gram-molecules  of  H2O,  and  (2)  one  gram-molecule  of, 
MgSO47H2O  in  93  gram-molecules  of  H2O,  contain  the  same 


1  Wied.  Ann.  18.  608. 

2  The  '  molecular '  heat  .of  the  solid  in  solution  may  be  determined  by  the  help 
of  this  formula,  provided  the  specific  heat  of  the  solvent  is  known :  see  Wiede- 
mann, loc.  cit. 

3  A  general  treatment  of  the  influence  of  temperature  on  the  thermal  values  of 
changes  occurring  between  liquids  will  be  found  in  Jahn,  loc.    cit.  Appendix  3, 
210—216. 

19—2 


CHEMICAL  STATICS.  [§  130 

quantities  of  MgSO4  and  H2O.    Now  from  observations  of  the 
specific  heat  of  solution  (i)  it  is  found  that 
<:(MgSO4+  ioo  H2O)  =  1761. 

But,  knowing  the  specific  heat  of  magnesium  sulphate, 
viz.  £(MgSO4)  =  27,  we  should  calculate  that 

<r(MgSO4+iooH2O)  =  27  +  (ioox  i8)  =  i82;. 

On  the  other  hand,  if  the  specific  heat  of  the  hydrate 
MgSO4  7H2O  is  determined,  and  from  this,  that  of  the  solution 
MgSO47H2O  +  93H2O  is  calculated,  we  get  this  result, 


The  observed  calorimetric  equivalent  is,  in  each  case,  less 
than  that  calculated  on  the  assumption  that  the  equivalent  of 
a  solution  is  equal  to  the  sum  of  the  equivalents  of  the  salt  and 
of  the  water  ;  but  the  difference  between  the  observed  and 
the  calculated  values  is  smaller  when  the  solution  is  made 
from  the  hydrated,  than  when  it  is  made  from  the  dehydrated 
salt1.  Thomsen2  considers  various  cases  of  this  kind,  and 
draws  the  general  conclusion,  that  the  change  in  the  thermal 
value  of  the  solution  of  a  hydrated  salt  in  water,  as  tempera- 
ture increases,  is  smaller,  the  greater  the  amount  of  water  of 
hydration  in  the  salt. 

When  compounds  other  than  hydrated  salts,  being  either 
solids,  liquids,  or  gases,  dissolve  in  water,  the  value  of  the 
thermal  change  also  varies  according  to  changes  of  tempera- 
ture, but  this  variation  is  sometimes  positive  and  sometimes 
negative  with  reference  to  the  temperature-change. 

130.     Any  chemical  reaction   occurs  only  within   certain 
limits   of  temperature;  by  passing  beyond  these  limits  it  is 
sometimes  possible  to   reverse  the  process   both  chemically 
and  thermally,  without  altering  the  nature  or  masses  of  the 
reacting  substances  ;  thus, 
at  ordinary  temperatures  2H2O  +  2C12  =  4HC1  +  O2  .....................  (i) 

but  at  about  200°  4HC1  +  O2  =  2H2O  +  2C12  ..................  (2); 


1  Hence  it  follows  that  the  specific  heat  of  the  water  in  a  solid  hydrated  salt  is 
less   than   the    specific    heat  of  the   same  water  when  the   salt    is  in  solution. 
(Thomsen,  loc.  cit.  1.  71.) 

2  loc.  cit.  I.  70—74. 


§  130]  APPLICATION    OF    PHYSICAL   METHODS.  2Q3 

if  reaction  (i)  is  expanded  thermally  it  becomes 

[2H2OAq,  2CPAq]  =  4[H,  Cl,  Aq]-2[H2,  O,  Aq]  =  2oj4oo  units+  : 
if  reaction  (2)  is  treated  in  the  same  way  we  have 

[4HC1,  O2]  =  2[H2,  O]-4[H,  Cl]  =  28,soo  units  +  (at  200°). 

When  we  deal  with  reactions  between  solids,  or  systems 
containing  solids  or  liquids,  the  numbers  obtained  by  measur- 
ing the  total  losses  or  gains  of 'heat  may  lead  to  erroneous 
conclusions  regarding  the  nature  of  the  chemical  reactions: 
thus  we  have  already  found  that  the  loss  of  energy  in  the 
formation  of  the  system  2H2O,  from  2H2  +  O2,  is  represented 
by  about  20,000  thermal  units  less,  when  the  entire  system 
is  maintained  throughout  the  reaction  in  the  gaseous  state, 
than  when  the  final  system  is  allowed  to  pass  into  the  liquid 
state.  Again  any  comparisons  or  contrasts  instituted  be- 
tween hydrochloric,  hydrobromic,  and  hydriodic  acids  from  a 
consideration  of  these  numbers, 

[H,  Cl]  =  22,ooo+;  [H,Br]  =  8,440+;  [H,  I]  =  6,050 - 
must  be  accepted  with  great  reserve,  because  no  indication  is 
given  in  these  equations  of  the  fact  that  at  ordinary  tem- 
peratures chlorine  is  a  gas,  bromine  a  liquid,  and  iodine  a 
solid  ;  the  reactions  formulated  appear  to  be  strictly  com- 
parable, whereas  they  really  present  wide  differences.  Another 
case  in  point  is  presented  by  these  numbers, 

(i)  [C,  0]  =  28,600+  ;        (2)  [C,  02]  =  97,000  +  . 

In  (i)  we  have  the  thermal  value  of  a  reaction  wherein  16 
grams  of  gaseous  oxygen  combine  with  12  grams  of  solid 
carbon  to  produce  28  grams  of  a  gaseous  compound  ;  in  (2) 
we  have  the  thermal  value  of  a  reaction  wherein  the  same 
weight  of  solid  carbon  combines  with  16x2  parts  by  weight 
of  gaseous  oxygen  to  produce  a  gaseous  compound.  The  con- 
clusion seems  inevitable  that  the  union  of  the  second  16 
grams  of  oxygen  with  carbon  is  attended  with  the  evolution 
of  much  more  heat  than  the  union  of  the  first  16  grams  of 
the  same  gas.  But  the  equation  [CO,O]  ==•  68,400,  which 
represents  the  union  of  a  second  quantity  of  16  grams  of 
oxygen  with  12  grams  of  carbon  already  combined  with  16 
grams  of  oxygen  in  a  gaseous  compound,  at  once  negatives 


CHEMICAL  STATICS.  [§  131 

this  conclusion,  and  rather  favours  that  which  would  regard 
the  number  136,800  (i.e.  68,400  x  2)  as  representing  the  true 
heat  of  combination  of  carbon,  i.e.  as  representing  the  thermal 
value  of  the  reaction  C  +  O2=CO2,  when  C  =  i2  grams  of 
gaseous  carbon.  The  following  numbers  shew  that  there  is 
a  close  analogy  between  the  thermal  reactions  of  gaseous  CO 
and  gaseous  H2  ; 

[C,  02]-2[CO,  0]  =  97,000  -(2x68,400) 

=  -  39,800, 
and  [C,  O2]-2[H2,  O]  =  97,000-  (2  x  68,400) 

=  -39,800; 

/.  [CO,  0]  =  [H«,  O]  ;  but  [H2,  O]=68,4oo, 
.-.    [CO,  0]  =  68,400. 

This  conclusion  is  confirmed  by  experiment.  Now,  the 
decomposition  of  gaseous  CO2  by  hot  C  has  the  same  thermal 
value  as  that  of  gaseous  H2O  by  hot  C  ;  thus 

andi[C°2'  C]=2[C'  °]-[C>  °2 
d,  C]  =  [C,   0]-[H2,  0 


Hence,  it  is  probable  that  the  thermal  value  of  the  forma- 
tion of  gaseous  CO2,  from  gaseous  C  and  O2,  is  double  that  of 
the  formation  of  gaseous  H2O,  from  gaseous  H2  and  O.  But 
the  latter  value  is  68,400,  therefore  the  former  is  probably 
136,800'. 

131.  Another  point  to  be  noticed  in  analysing  thermal 
measurements  of  chemical  processes  is,  that  the  ordinary 
notation  usually  represents  a  chemical  change  as  a  much 
simpler  phenomenon  than  it  really  is.  Most  chemical  re- 
actions are  accomplished  only  by  employing  'an  excess/ 
sometimes  a  large  excess,  of  one  or  more  of  the  reacting  sub- 
stances: thus  the  equation 

AgCl  +  HI  (grams)  =  AgI  +  HCl 

would  more  nearly  express  the  distribution  of  the  masses  of 
the  reacting  bodies  if  it  were  written 

x  AgCl  +  *'H  I  =  x"  Agl  +  *"H  Cl  +  (x  -  x"}  AgCl  +  (x1  -  x"}  H  I  . 

1  See  Mendelejeff,  abstract   of  Russian  paper  in    Ber.    15.  1555  ;    or   C.  £. 
Journal,  Abstracts  for  1882,  916. 


§  132]  APPLICATION   OF   PHYSICAL   METHODS.  295 

Potilitzin  has  investigated  this  subject  of  the  relations  be- 
tween the  thermal  value  of  a  change  and  the  masses  of  the 
changing  substances1.  The  heat  of  formation  of  a  metallic 
chloride  is  as  a  rule  greater  than  that  of  the  corresponding 
bromide, 

[MBr,  C1]  =  [M,  C1]-[M,  Br]>o  : 

Again  generally  speaking  it  is  true  that 

[MBr,  HC1]  =  [M,  C1]  +  [H,  Br]-[M,  Br]-[H,  Cl]<o; 
e.g.  [AgBr,HCl]  =  6,9oo-  ;  [KBr,  HC1]  =  3,250-  ;  [NaBr,  HCl]  =  i,6oo-. 

It  would  therefore  appear  probable  that  chlorine  should  de- 
compose metallic  bromides,  but  that  hydrochloric  acid 
should  not  react  on  these  salts. 

But  Potilitzin's  experiments  shew  that  the  reaction 


proceeds  at  275  —  300°  when  MCI  and  Br  are  employed  in 
equivalent  quantities,  (M  =  K,  Na,  or  Ag),  and  also  that  when 
MBr  and  Cl  react  in  equivalent  quantities  the  whole  of  the 
bromine  is  not  replaced  by  the  chlorine. 

By  increasing  the  amount  of  bromine,  relatively  to  MCI,  in 
the  reaction  above  formulated,  more  MBr  is  produced  until 
a  limit  is  reached,  whereat  equilibrium  is  established.  This 
equilibrium  is  not  overthrown  even  by  increasing  the  mass  of 
bromine,  raising  the  temperature,  and  prolonging  the  time  of 
action. 

132.  I  think  the  position  has  now  been  clearly  established 
that  the  thermal  value  of  a  chemical  change,  even  of  a  simple 
reaction  between  gaseous  substances,  really  represents  the 
sum  of  various  changes,  some  of  which  have  a  positive  and 
others  a  negative  value.  Assuming  that  in  any  case  it  is 
possible  to  separate  the  gain  or  loss  of  energy,  measured 
thermally,  during  a  definite  chemical  reaction,  into  a  portion 
representing  physical  changes,  and  another  portion  repre- 
senting purely  chemical  changes,  it  is  nevertheless  generally 
the  case,  that  the  latter  portion  of  the  total  energy-change 
must  itself  be  analysed,  before  an  accurate  and  precise  appli- 
cation of  the  thermal  value  can  be  made.  For,  assuming  that 

1  See  abstract  in  Be>\  14.  2044  ;  and  16.  918  ;  also  16.  3051. 


296  CHEMICAL  STATICS.  [§  132 

we  have  made  due  allowance  for  the  influence  of  the  masses 
of  the  reacting  substances,  and  for  the  possible  formation 
and  decomposition  of  molecular  groups  during  the  reaction, 
there  yet  remains  the  important  consideration,  that  heat  is 
absorbed  or  evolved,  not  only  in  decomposing,  or  producing, 
compounds,  but  also  in  reactions  of  decomposition  or  forma- 
tion of  elements,  which  take  part  in  the  chemical  process. 
Let  us  analyse  a  comparatively  simple  reaction  ; 


When  this  is  expanded  thermally  we  have 

OJTO,  2C12]  =  4[H,  Cl]  +  [0,  0]-2[H»,  0]-2[C1,  Cl]. 
That  is  to  say,  heat  is  absorbed  in  separating  each  chlorine 
molecule  into  atoms,  and  heat  is  evolved  in  the  union  of  each 
pair  of  oxygen  atoms  to  form  a  molecule. 

Let  us  take  an  apparently  more  simple  instance 
[H2,  C12]=  44,000  units  +. 

Remembering  the  fundamental  distinction  between  atoms 
and  molecules,  and  moreover  bearing  in  mind  the  fact  that 
the  molecules  of  hydrogen  and  chlorine  are  both  diatomic,  we 
may  expand  this  equation  thus 

[H*,  Cl']  =  2[H,  C1]-[H,  H]-[C1,  Cl]  =  44,000. 

But  we  do  not  know  the  true  thermal  value  of  any  one  of  the 
three  parts  of  this  reaction  ;  when  therefore  we  write  [H2,  Cl2] 
=  44,000,  we  express,  in  a  shorter  form,  the  fact,  that  when 
2  grams  of  gaseous  hydrogen  combine  with  71  grams  of  gaseous 
chlorine  to  produce  73  grams  of  gaseous  hydrochloric  acid,  at 
ordinary  temperatures,  44,000  gram-units  of  heat  are  evolved. 

As  long  as  thermal  measurements  are  regarded  in  this 
way  they  convey  precise  and  important  information.  But  we 
want  something  more  than  this,  we  desire  to  have  some  light 
thrown  on  the  rationale  of  chemical  changes.  Now  our  most 
far-reaching  conceptions  in  chemistry  are  based  on  the  dis- 
tinction implied  in  the  terms  atom  and  molecule  ;  until  then 
this  distinction  is  practically  recognised  in  thermal  chemistry, 
we  cannot  expect  any  great  advances  to  be  made  in  applying 
the  mass  of  data  already  accumulated  to  questions  of  chemical 
actions  and  reactions.  The  want  of  any  means  of  determining 


§  133]  APPLICATION   OF   PHYSICAL   METHODS.  297 

the  thermal  values  of  the  decomposition  of  elementary 
molecules,  and  the  combination  of  elementary  atoms,  is  felt 
even  more  when  an  attempt  is  made  to  apply  the  data  of 
thermal  chemistry  to  the  questions  which  are  included  und< 
general  title  of  chemical  kinetics.  This  subjectwill  be  dk 
in  the  second  part  of  this  work.  At  present  I  would 
student  against  employing  the  term  atom  and  molec 
loose  way,  and  at  the  same  time  remind  him  that 
allow  a  certain  degree  of  elasticity  to  our  use  of  molecular 
and  atomic  conceptions,  we  cannot  make  much  use  of  the 
measurements  which  have  been  so  plentifully  amassed  by  the 
aid  of  the  calorimeter. 

133.  In  the  Introduction  to  volume  I.  of  his  Essai  de 
me'canique  chiinique,  Berthelot  lays  down  three  fundamental 
principles  of  thermal  chemistry  [p.  xxviii — xxix]. 

(1)  The  quantity  of  heat  evolved  in  a  reaction  measures 
the  sum  of  the  physical  and  chemical  changes  which  occur  in 
that  reaction. 

(2)  The  total  thermal  value  of  a  reaction  is  dependent  only 
on  the  initial  and  final  states  of  the  changing  system. 

(3)  Every  chemical  change  accomplished  without  addition 
of  energy  from  without,  tends  to  the  formation  of  that  body  or 
system  of  bodies  the  production  of  which  is  accompanied  by 
the  evolution  of  the  maximum  quantity  of  heat. 

The  first  and  second  principles  have  already  been  illus- 
trated and  discussed.  The  third,  under  the  name  of  the  "  law 
of  maximum  work  "  forms  the  basis  of  all  Berthelot's  thermo- 
chemical  generalisations.  It  is  stated  in  an  even  more  rigid 
form  as  the  theorem  of  the  necessity  of  reactions *,  "  Every 
chemical  change  which  can  be  accomplished  without  the  aid 
of  a  preliminary  action  or  the  addition  of  energy  from  without 
the  system,  necessarily  occurs  if  it  is  accompanied  by  disen- 
gagement of  heat." 

This  so-called  law  of  maximum  work  cannot  be  fully  dis- 
cussed without  introducing  facts  and  considerations  belonging 
to  the  domain  of  chemical  kinetics2;  but  I  think  that  if 

1  loc.  cit.  ;  Introduction,  p.  xxix.,  also  2.  422. 

2  See /<?*/,  Book  II.  chapter  ill.  par.  241. 


298  CHEMICAL   STATICS.  [§  r33 

the  fundamental  distinction  between  atom  and  molecule  is 
clearly  grasped,  it  will  at  once  be  seen  that  Berthelot's  state- 
ment is  too  general  to  be  of  much  service  in  elucidating  the 
mechanism  of  chemical  change. 

Berthelot's  law  is  simply  a  crude  application  of  the  prin- 
ciple of  the  degradation  of  energy  ;  the  principle,  namely,  that 
energy  always  tends  to  run  down  from  a  more  available  to  a 
less  available  form.  Inasmuch  as  the  production  of  a  chemical 
compound,  with  evolution  of  heat,  is  an  instance  of  such  running 
down  of  energy,  from  the  form  of  chemical  affinity  to  that  of 
heat,  it  follows  that  the  reversal  of  this  process  will  require  the 
expenditure  of  work.  But  the  law  of  maximum  work  does 
not  attempt  to  analyse  the  expression  chemical  affinity.  Under 
this  term  Berthelot  includes  actions  and  reactions  of  different 
kinds.  This  is  at  once  apparent  from  the  statement  in  the 
Essa?,  that  the  first  fundamental  principle  of  thermal  che- 
mistry, viz. — "  the  quantity  of  heat  evolved  in  a  reaction  mea- 
sures the  sum  of  the  physical  and  chemical  changes  which  occur 
in  that  reaction  " — furnishes  the  measure  of  chemical  affinities2. 

Berthelot's  work  is  saturated  with  the  conceptions  of  the 
molecular  theory :  but,  by  some  fatal  perverseness,  he  refuses 
to  apply  this  theory  to  chemical  phenomena.  While  recog- 
nising the  existence  of  molecules,  and  building  his  generalisa- 
tion on  a  molecular  foundation,  he  refuses  to  accept  the 
conception  of  atom,  or  rather  he  hopelessly  confuses  it  with 
that  of  equivalent.  The  molecule  is  for  him  a  definite  and 
definable  portion  of  matter,  the  parts  of  the  molecule  are  only 
numbers. 

If  by  chemical  affinity  is  meant  an  action  and  reaction 
between  atoms,  then  the  principle  already  quoted  certainly 
does  not  afford  a  measure  of  this  affinity. 

Berthelot's  law,  then,  appears  to  be  a  definite  statement 
applicable  to  chemical  reactions ;  but  more  precise  investi- 
gation shews  that  the  application  is  only  possible  when 
'  chemical '  is  used  in  a  vague  way  as  including  much  that 
is  usually  called  *  physical.' 

1  Introduction,  p.  xxviii. 

2  „'  Ce  principe  fournit  la  mesure  des  affinit 


§133]  APPLICATION   OF   PHYSICAL  METHODS.  299 

The  principle  of  the  degradation  of  energy  is  a  highly 
generalised  statement  applicable  to  certain  cycles  of  change ; 
Berthelot  attempts  to  apply  it  to  parts  of  such  cycles,  forget- 
ting that  what  is  true  of  the  whole  is  not  necessarily  true  of 
the  parts. 

Thirty  years  ago  Thomsen  *  generalised  the  relations  be- 
tween chemical  action  and  thermal  change  in  the  statement, 
"Every  simple  or  complex  reaction  of  a  purely  chemical  kind 
is  accompanied  by  evolution  of  heat." 

If  by  a  reaction  '  of  a  purely  chemical  kind '  is  meant  the 
combination  of  atoms  to  form  molecules,  no  objection  can  be 
made  to  this  statement ;  we  recognise  its  importance  and 
universality,  as  we  recognise  the  same  qualities  in  such  state- 
ments as  '  all  men  are  mortal/  or  '  no  white  men  are  black.' 
But  we  may  doubt  its  utility.  Thomsen  explains  that 
'  reactions  of  a  purely  chemical  kind'  are  those,  which  proceed 
without  addition  of  energy  from  sources  external  to  the 
system,  and  consist  only  of  the  strivings  of  atoms  towards 
some  stable  equilibrium3.  On  the  other  hand  a  chemical 
system  may  be  raised  to  a  temperature  such  that  its  consti- 
tuents are  no  longer  stable,  and  reactions  may  then  occur 
with  expenditure  of  external  energy ;  but  these  changes 
do  not  depend  solely  on  mutual  atomic  attractions.  But 
actions  '  of  a  purely  chemical  kind '  never  occur,  except  as 
parts  of  cycles  of  reactions,  which  include  changes  that  do  not 
consist  '  solely  of  the  strivings  of  atoms  towards  more  stable 
equilibrium.'  Hydrogen  and  oxygen  do  not  combine  to  form 
water,  neither  do  chlorine  and  hydrogen  combine  to  form 
hydrochloric  acid,  without  the  addition  of  energy  from  ex- 
ternal sources. 

Statements  such  as  those  quoted  from  Thomsen  or  Berthe- 
lot are  true,  only  when  an  arbitrary  separation  is  made  of 
chemical  changes  into  two  parts,  and  one  of  these  parts  is 

1  See  Thermochemische  Untersuchungen,  1.  12 — 16. 

2  loc.  cit.  1.  1 6. 

3  "  Der  chemische  Process  ist  rein  chemischer  Natur,  wenn  er  ohne  Aufwand 
fremder  Energie  verlalift,  und  nur  durch  das  Streben  der  Atome  nach  mehr  stabilen 
Gleichgewichtslagen  zu  Stande  kommt." 


300  CHEMICAL   STATICS.  [§  134 

alone  called  chemical.  Every  chemical  change,  however 
simple,  consists  of  at  least  two  parts,  the  first  of  which  is  the 
necessary  antecedent  of  the  second ;  the  law  of  maximum  work 
ignores  this  duality,  or,  it  might  be  more  accurate  to  say, 
the  law  assumes  that  the  second  part  of  a  chemical  process 
can  occur  without  the  first.  Every  process  of  chemical  change 
may  be  compared  to  the  flight  of  a  stone  from,  and  its  return 
to  the  surface  of  the  earth.  During  the  first  part  of  this  pro- 
cess there  is  a  continual  transference  of  kinetic  energy  from 
the  moving  stone  to  the  surrounding  medium,  and  during  the 
second  part,  a  continual  transference  from  the  medium  to  the 
stone,  until  the  stone  comes  to  rest,  when  its  energy  becomes 
a  part  of  the  total  energy  of  the  system,  earth  +  stone.  If  the 
final  resting-place  of  the  stone  is  nearer  the  centre  of  the 
earth  than  the  spot  from  which  it  was  projected  on  its  upward 
flight,  then  the  stone  contains  less  energy,  relatively  to  sur- 
rounding systems,  at  the  close  of  the  transaction  than  at  the 
beginning.  On  the  other  hand,  if  the  starting-point  is  nearer 
the  earth's  centre  than  the  final  point  of  rest,  then  the  trans- 
action has  resulted  in  gain  of  energy  to  the  stone.  In  both 
cases  the  second  part  of  the  transaction,  that  which  occurs 
between  the  turning-point  and  the  final  resting-point  of  the 
stone,  is  attended  with  loss  of  energy ;  but  this  second  part 
does  not  represent  the  complete  transaction.  The  law  of 
maximum  work  is  applicable  only  to  the  second  part.  And 
moreover  this  law  ignores  the  fact  that  the  stone  (or  chemical 
system)  does  not  leave  its  initial  point  of  rest  of  its  own 
accord ;  the  law  assumes  that  no  work  need  be  done,  no 
energy  expended,  in  the  passage  of  the  (stone  or  system) 
from  its  original  position  to  that  at  which  the  energy-relations 
between  it  and  surrounding  systems  come  within  the  cogni- 
sance of  the  law. 

134.  An  attempt  has  been  made  by  Thomsen  to  measure 
the  thermal  values  of  the  first  parts,  i.e.  separation  of  molecules 
into  atoms,  of  certain  changes  which  result  in  the  production 
of  hydrocarbons.  Attention  has  already 1  been  drawn  to  this 
investigation. 

1  See  ante,  chapter  n.  section  iv.  par.  84. 


§  134]  APPLICATION    OF   PHYSICAL  METHODS.  3<DI 

Thomsen's  results  are  obtained  by  the  aid  of  many  hypo- 
theses, some  of  which  appear  to  be  quite  unjustified  by  facts1. 
Among  such  hypotheses  I  would  place ; — 

(1)  The    assumption    that   the    molecule   of  carbon    is 
diatomic : 

(2)  The   assumptions   on  which  the  reasoning  is  based 
whereby  the  thermal  value   of  the  process  resulting  in  the 
formation  of  this  diatomic  molecule  from  amorphous  carbon 
is  calculated. 

Thus,  comparing  the  reactions 

(a}    C2H2  +  H2  =  C2H4,     (b)   C2H4  +  H2=C2H6,    (c)  C2H6+  H2=2CH4, 
it  is  found  (assuming  2CH4  to  be  equal  to  C2H8)  that  the  mean 
thermal  value  for  the  addition  of  H2=  HS/o  gram-units. 

But,  at  the  same  time 
the  value  of  the  reaction  [C2H4,  H2]  is  found  to  be  equal  to 

[CW,  H2]  +  (2  x  14,570), 

and  the  value  of  the  reaction  [C2H2,  H2]  is  found  to  be  equal  to 
[C2,  H*]  +  (3x14,570)- 

Hence,  if  we  assume  that 

the  value  of  the  reaction  [C2,  H2]  is  equal  to  [C,  C]  +  (4X  14,570), 

it  follows  from  the  known  value  of  the  reaction  [C2,  H2],  that 

[C,  C]=  106,630  units2. 

But  this  value  [C,  CJ  represents  the  sum  of  two  thermal 
changes,  (a)  the  heat  absorbed  in  gasifying  amorphous  carbon 
and  separating  the  molecule  into  its  pair  of  constituent  atoms, 
and  (b)  the  heat  evolved  in  the  falling  together  of  a  pair  of 
atoms  to  form  the  (hypothetical)  diatomic  gaseous  molecule  C2. 
Thomsen  attempts  to  determine  the  value  of  (a) ;  but  in  doing 
this  he  makes  another  startling  assumption  viz. 
that  because         [C,  O2]  =  96,960,  and  [CO,  O]  =  68,080, 
therefore  [C,  O]  =  [C,  O2]-[CO,  O]  =  28,880. 

1  Thomsen's  papers  will  be  found  in  Ber.  13.  1321  and  1388  ;   and  15.  318 
(also  Journal  fur  prakt.  Chemie.  131.  157).     A  much  condensed  account  is  given 
in  Thomsen's    Thcrmochemische  Untersuchungen,  2.  96 — 113.     A  clear  and  full 
account  of  Thomsen's  investigation,  by  J.  P.  Cooke,  appeared  in  Amer.  Journal 
of  Science  and  Arts  [3],  21.  87 — 98. 

2  Thomsen  uses  this  value  to  calculate  the  reaction  [C2,  H2],  [C2H2,  H2]  &c., 
but  of  course  the  results  agree  with  those  actually  found  by  experiment. 


302  CHEMICAL  STATICS.  [§  134 

Thomsen  apparently  forgets  that  the  reaction  [C.  O2] 
represents  the  production  of  44  grams  of  gaseous  carbonic 
anhydride  from  32  grams  of  gaseous  oxygen  and  12  grams 
of  solid  carbon;  whereas  the  reaction  [CO,  O]  represents 
the  addition  of  16  grams  of  gaseous  oxygen  to  28  grams  of 
gaseous  carbon  monoxide1. 

Some  very  strange  results  are  obtained  by  Thomsen:  e.g. 
he  thinks  it  very  probable  that  [O,C,O]  =  2  [C,O],  but  the 
numbers  on  which  his  own  hypothesis  is  based  shew  that 
[O,C,O]-  2  [C,O]  =  39,200  +;  in  fact  this  value  is  constantly 
used  throughout  the  investigation.  Again  the  calculated  pro- 
bable value  of  the  heat  absorbed  in  separating  two  carbon 
atoms  from  amorphous  carbon  is  77,800  units,  but  to  do 
this,  and  also  to  form  the  diatomic  molecule  C2  from  these 
separated  atoms,  requires  an  absorption  of  106,630  units, 
therefore  the  falling  together  of  two  carbon  atoms  to  form  a 
molecule  is  attended  with  the  absorption  of  28,830  units  of 
heat. 

Later  on  we  find  that  the  strange  behaviour  of  the  atoms 
of  carbon  is  to  be  traced  to  the  vagaries  of  their  'bonds.' 
Two  atoms  of  carbon  may  unite,  on  the  bond  hypothesis,  in 
four  ways  : — 

(1)  One  bond  of  each  atom  is  satisfied  by  one  bond  of  the  other  atom: 

heat  evolution  =  about  14,500  units. 

(2)  Two  bonds  of  each  atom  are  satisfied  by  two  bonds  of  the  other  atom  : 

heat  evo lution=  14,500  units. 

(3)  Three  bonds  of  each  atom  are  satisfied  by  three  bonds  of  the  other 

atom:  heat  evolution  =  Q. 

(4)  Four  bonds  of  each  atom  are  satisfied  by  four  bonds  of  the  other 

atom  :  heat  absorption  —  about  28,000  units. 

It  also  follows  from  Thomsen' s  numbers  that  [C,C]<[C,  H], 
and  that  [C,O]  >  [C,C]  (when  C  +  C  forms  C  -  C). 

As  might  be  expected,  the  application  by  Thomsen  of  his 
hypothetically  determined  values  leads  to  somewhat  anomalous 
results.  The  calculated  heats  of  formation  of  hydrocarbons 
'sometimes  agree  fairly  well  with  the  observed  numbers, 
sometimes  there  are  marked  differences  between  the  two 

1  See  also  ante,  this  section,  par.  130. 


§  134]  APPLICATION   OF   PHYSICAL  METHODS.    .  303 

numbers.  Thus,  comparing  the  observed  and  calculated  heats 
of  combustion  (because  these  are  the  bases  for  calculating 
heats  of  formation)  of  benzene  and  dipropargyl,  we  have  this 
result. 

I.    HEAT  OF  COMBUSTION  OF  BENZENE  (C6H6). 

On  the  assumption  that  each  carbon  On  the  assumption  that  each  carbon 

atom   is  trivalent  (or,   that   the  atom  is  tetravalent  (or,  that  the 

molecule     contains     3     '  double  molecule     contains     9     '  single 

bonds '    and    3    '  single   bonds '  bonds '  between  carbon  atoms), 
between  carbon  atoms). 

Calculated.         Difference.        Observed.                 Calculated.          Difference.  Observed. 

844,500          -38,700        805,800   (l)           800,400         +    5,400  805,800   (l) 

844,500           -56,500        788,000   (2)           800,400         -I2,40O  788,000   (2) 
(i)  Earlier,  (2)  later  observations. 

II.    HEAT  OF  COMBUSTION  OF  BENZENE  AND  DIPROPARGYL  (C6H6). 

Berthelot's  numbers.  Observed  Difference.  Thomsen's  numbers. 

dipropargyl  =  853,6oo\      ^_  ^Q_  / 883,200  =  dipropargyl 

benzene       =776,ooo<x  ^788,000  =  benzene 

Calculated  difference,  (i)  on  the  assumption  that  each  carbon  atom  in  the 

benzene  molecule  is  tetravalent  =  88,200. 

Calcidated  difference  (2)  on  the  assumption  that  each  carbon  atom  in  the 
benzene  molecule  is  trivalent  =  44,100. 

The  numbers  representing  the  heats  of  combustion  of 
dipropargyl  and  benzene  obtained  by  Berthelot,  are  con- 
siderably greater  than  those  obtained  by  Thomsen ;  the 
difference  amounts,  in  the  former  case,  to  29,600,  and  in  the 
latter  case  to  12,000  units. 

It  would  evidently  be  absurd  to  draw  any  precise  con- 
clusions regarding  the  structure  of  the  molecules  of  benzene 
and  dipropargyl  from  these  results1. 

Two  general  conclusions  may,  I  think,  be  drawn  from 
Thomsen's  investigation  ;  (i)  that  the  energy-changes  attend- 
ing the  formation  of  isomeric  molecules  are  correlated,  not 
only  with  the  valencies  of  the  constituent  atoms,  but  also  with 
the  distribution  of  the  atomic  interactions2;  (2)  that  the  use  of 

1  For  a  criticism  of  Thomsen's  conclusions  regarding  the  structure  of  hydro- 
carbons see  Mendelejeff,  Ber.  15.  1555 ;  or  C.  S.  Journal,  Abstracts  for  1882,  916. 

2  Lothar  Meyer,  Die  Modernen  Theorien  der  Chemie,  424,  puts  the  conclusion 
to  be  drawn  regarding  the  'linking'  of  two  carbon  atoms  thus,   "what  we   call 


304  CHEMICAL   STATICS.  [§  135 

that  nomenclature  which  is  founded  on  the  hypothesis  of 
bonds  ought  to  be  abandoned1. 

135.  A  few  generalisations  have  been  established  re- 
garding the  connection  between  the  structure  and  the  boiling 
point  of  carbon  compounds.  Thus  the  difference  between 
the  boiling  points  of  two  consecutive  members  of  an  homo- 
logous series  of  carbon  compounds  is  frequently  about  19°: 
but  the  numbers  actually  obtained  shew  that  variations  in 
the  boiling  points  are  connected  with  variations  other  than 
those  of  molecular  weight.  Goldstein2  attempts  to  shew  that 
the  proportion  between  the  numbers  of  hydrogen  and  carbon 
atoms,  besides  the  total  number  of  these  atoms,  influences  the 
boiling  points  of  the  members  of  an  homologous  series.  Hydro- 
carbons of  analogous  constitution  must  be  compared,  i  e.  normal 
hydrocarbons  must  be  compared  with  normal, 
e.g.CH3-CH2-CH2-CH3withCH3-CH2-CH2-CH2-CH3; 
or  iso-with  iso-hydrocarbons,  e.g. 

CH(CH3)2-CH2-CH3withCH(CH3)2-CH2-CH2-CH3; 
nor  can  the  differences  between  the  boiling  points  of  normal, 
be  compared  with  the  differences  between  the  boiling  points 
of  iso-hydrocarbons. 

Goldstein  investigates  the  change  of  boiling  point  in  the 
series  of  normal  paraffins  :  i.e.  hydrocarbons  of  the  form 
CH3  -  (CH2X  -  CH3  [or  CH3  -  CHR'  -  CHJ.  He  gives  the 
formula 


where  B.  P.  =  boiling  point  required,  b.  p.  =  boiling  point  of 
the  paraffin  containing  CH2  less  than  that  whose  B.  P.  is  re- 
quired, and  n  =  number  of  atoms  of  carbon  in  the  molecule  of 
the  paraffin  whose  B.  P.  is  known.  Thus,  the  boiling  point  of 
C5H12  (i.e.  CH3(CH2)3CH3)  is  39°'o;  required  the  boiling  point 
of  C6HM(i.e.  CH3(CH2)4CH3).  ' 

double,  or  triple,  linking  of  atoms,  does  not  consist  of  a  repetition  of  the  process 
which  we  call  single  linking." 

1  See  ante,  chapter  II.  section  IV.  par.  84. 

2  Ber.  12.  689  :  also  abstract  of  paper  in  Russian,  C.  S.  Journal  Abstracts 
for  1882,  374- 


§135]  APPLICATION  OF  PHYSICAL  METHODS.  305 

B.P.  required  =, 


=  39+I9+I2'66 

=  70°  '66.  B.P.  observed  =70°  '6. 

Goldstein  calculated  the  B.P.  of  normal  heptane  (C7H16) 
to  be  98°'65  ;  shortly  after  this,  the  paraffin  was  obtained  in 
quantity  by  Thorpe,  and  the  boiling  point  was  found  to  be 

98°'S- 

The  same  formula  appears  to  hold  good  for  determining 
the  difference  between  the  boiling  points  of  any  two  consecutive 
iso-paraffins  belonging  to  the  form  CH  (CH3)^—  (CH^—  CH3. 
Thus, 

B.P.    Difference. 


'%..calcu.ateddifference=3I'-66. 


c 

If  this  is  so,  it  follows  that  the  difference  between  the 
boiling  point  of  a  normal  -  and  its  corresponding  iso-paraffin 
(of  this  form)  must  be  the  same  whatever  be  the  molecular 
weight  of  the  two  isomerides.  Experiment,  so  far  as  it  has 
gone,  seems  to  confirm  this  result;  thus, 

T^,.m,,io  Difference  between  B.P.  of  normal 

Formula'  and  iso-paraffin. 

C5H12  8°«5 

C6H14  8°-6 

C7H16  8-5 

Kahlbaum  l  has  made  some  determinations  of  the  ratio 
between  the  change  in  the  boiling  points  of  ethylic  alcohols 
and  acetic  acids,  and  the  diminution  of  pressure,  and  has 
concluded  that  a  definite  relation  exists  between  at  least  the 
empirical  formula  of  a  compound  and  the  ratio  in  question. 

We  have  very  little  precise  knowledge  regarding  the 
boiling  points  of  isomeric  hydrocarbons.  From  the  data 
accumulated  it  has  been  concluded,  that,  of  two  or  more 
isomeric  hydrocarbons,  that  one  has  the  lowest  boiling  point, 
the  molecule  of  which  is  characterised  by  containing  the 
greatest  number  of  '  side  chains'2.  Thus 

1  Ber.  16.  2476:  17.  1245,  and  1263. 

2  For  data  see  Naumann,  loc.  cit.  pp.  168  —  172. 

M.  C.  20 


306  CHEMICAL    STATICS.          [§§  136,  137,  138 

Pentane  (C5H12).  B.P. 

(a)  normal :— CH3(CH2)3  -  CH3  39° 

(ft)  isopropyl-methylmethane  : — CH2-CH(CH3)2- CH3  3O°'5 
(c)  tetramethylmethane  :— C(CH3)4  9°'5 

Hexane  (C6H14). 

(a)  normal :— CH3(CH2)4CH3  7o°'5 

(J)  isopropyl-ethylmethane  :— CH2  -  CH(CH3)2 -  C2H5  62° 

(c]  di-isopropyl :— CH(CH3)2-CH(CH3)2  58° 

(d)  trimethyl-ethylmethane  :— C(CH3)3(C2H5)  43°— 48° 

136.  In  this  section  I  have  tried  to  trace  some  of  the 
connections  between  the  results  of  thermal  measurements  of 
chemical  phenomena  and  the  statical  aspects  of  these  pheno- 
mena. We  have  found  that  every  chemical  phenomenon  is  a 
complex  occurrence,  and  that  it  is  almost  impossible  fully  to 
differentiate  those  portions  which  would  more  appropriately  be 
called  physical,  from  those  which  are  undoubtedly  chemical. 
We  have  also  found  that  thermal  measurements,  being  essen- 
tially measurements  of  changes  of  energy,  are  intimately  con- 
nected with  problems  belonging  to  chemical  kinetics,  and  that 
until  we  have  some  precise  knowledge  regarding  chemical 
affinity  we  are  not  in  a  position  fully  to  discuss  the  data  of 
thermal  chemistry. 


SECTION  II.     Optical  Methods. 

137.  In  this  section  I  wish  to  give  some  account  of  the 
attempts  which  have  been   made  to  elucidate  the   relations 
existing  between  (i)  the  refractive  powers,  (2)  the  power  of 
rotating   a    ray   of  polarised    light,    and    (3)   the   absorption 
spectra,  and  the  composition  of  certain  chemical  compounds. 
The  subject  is  more  limited  than  that  considered  in  the  first 
section  of  the  present  chapter ;  it  belongs,  more  completely 
than  thermal  chemistry,  to  the  domain  of  chemical  statics, 
although  like  other  questions  in  chemical  science,  it  is  under 
certain  aspects  best  considered  from  a  kinetical  point  of  view. 

138.  Let  a  ray  of  light  pass  from  air  into  a  liquid  medium 
denser  than  air ;  let  the  angle  of  incidence  =  i,  and  the  angle 


§  138]  APPLICATION    OF   PHYSICAL   METHODS.  307 

of  refraction  =  r\  then  —  —  =  /u.  =  refractive  index  of  the  me- 
dium. 

Let  the  light  employed  consist  only  of  light  of  one 
wave-length,  and  let  the  liquid  medium  consist  of  a  single 

CLL  ~  \\ 
^        j    was 

called  by  Gladstone  and  Dale1  the  specific  refractive  energy  of 
the  liquid  examined,  (d=  density  of  the  liquid  referred  to 
water  as  unity).  Landolt2  called  the  product  obtained  by 

multiplying  (          j  into  the  molecular  weight  of  the  liquid, 

i.e.  (  ,  j  M,  the  refraction  equivalent  of  the  liquid  compound 
in  question. 

(LL  —  I\ 
—r-  J  was  said  by  Gladstone  and  Dale  to 

be  independent  of  temperature3. 

The  refraction-equivalent  of  the  molecule  of  a  chemical 
compound  is  generally  said  to  be  the  sum  of  the  refraction- 
equivalents  of  the  atoms  which  compose  the  molecule :  or 
the  refraction-equivalent  of  a  mixture  is  the  sum  of  the 
equivalents  of  its  components4. 

But  objection  has  been  taken  by  Wiedemann5  to  the  use 

of  the  constant    (      ,    j  M  in  attempts  to  trace  connections 

between  the  composition  and  the  optical  properties  of  com- 
pounds. Any  relations  which  appear  to  exist  between  mole- 
cular composition  and  physical  properties  must,  it  is  urged, 
be  formal  rather  than  real  relations,  as  long  as  the  pro- 
perties of  the  molecule  are  assumed  to  be  the  sum  of  the 
properties  of  the  atoms.  Physical  constants  ought  to  be 
employed  which  determine  the  properties  of  atoms. 


1  Proc.  R.  S.  12.  448,  and  Phil.  Trans.  153.  317. 

2  Fogg.  Ann.  122.  545  ;  and  123.  595. 

3  See  Proc.  R.  S.  18.  49  ;  and  also  Phil.  Trans.  160.  9. 

4  See  especially  Landolt,  Pogg.  Ann.  123.  623. 

5  Ber.  15.  467. 

20—2 


308  CHEMICAL   STATICS.  [§  138 

Now   A.   Lorenz   and    H.   Lorenz1,  within   the  last   few 
years,  independently  deduced  the  expression 


from  the  general  principles  of  the  undulatory  theory  of  light 
(and  more  especially  from  Maxwell's  electromagnetic  theory), 
as  giving  a  statement  of  the  relation  between  the  velocity  of 
transmission  of  light,  and  the  density  of  the  liquid  medium 
through  which  it  is  propagated. 

Landolt2  has  applied  the  two  formulae 


to  calculate  the  refraction-equivalents  of  mixtures,  on  the  sup- 
position that  these  equivalents  are  equal  to  the  sums  of  the 
equivalents  of  the  constituents,  and  has  found  that  the  results 
are  the  same  whichever  formula  is  adopted  ;  and  moreover 
that  the  observed  agree  with  the  calculated  results,  except 
when  very  strongly  refractive  liquids,  such  as  carbon  di- 
sulphide,  are  employed.  Hence  Landolt  argues  that  con- 
clusions regarding  the  connection  between  the  molecular  com- 
position and  the  refraction-equivalents  of  compounds,  deduced 
by  aid  of  the  first  (purely  empirical)  formula,  are  confirmed 
by  the  use  of  the  second  formula,  which  is  deduced  from 
the  general  principles  of  the  undulatory  theory  of  light. 

But  neither  formula  is  independent  of  dispersion.  It  is 
however  possible  by  the  use  of  Cauchy's  formula  to  arrive  at 
an  expression  for  the  refraction-equivalent  which  is  practi- 
cally independent  of  dispersion3.  This  expression  may  be 
formulated  as 


1  Wied.  Ann.  9.  641  ;  and  11.  70. 

2  Ber.  15.  1031. 

3  For  details  consult  a  text-book  on  Optics  (e.g.  see  Glazebrook's  Physical 
Optics,  pp.  244  —  46).     But  it  appears,  from  an  investigation  by  Langley,  that  this 
formula  gives  erroneous  results  '  when  extended  far  beyond  the  limits  within  which 
the  observations  on  which  it  is  founded  are  made.'     See  Phil.  Mag.  for  March 
1884;  or  in  full,  Ann.  Phys.  Chim.  (6)  2.  145.     Hence,  the  apparently  anomalous 
refraction-equivalents  of  some  carbon  compounds  (see  /&$•/.,  par.  142)  may  be  due 
to  the  very  great  dispersion  which  is  noticed  in  these  cases.     See  Gladstone,  C.  S. 
Journal.  Trans,  for  1884.  241. 


§  139]  APPLICATION   OF   PHYSICAL  METHODS.  309 

where  A  M  =  refractive  index  of  the  theoretical  ray  of  infinite 
wave-length. 

We  have  then  the  four  expressions  for  rinding  the  refrac- 
tion-equivalent of  a  liquid  compound  ; 


(i)1  M=W          (2) 

(4) 


The  values  obtained  by  equations  (3)  and  (4)  are  about 
one-third  less  than  those  obtained  by  the  use  of  equations 
(i)  and  (2). 

These  formulae  yield  expressions  for  finding  the  refraction- 
equivalent  of  each  constituent  of  a  mixture,  or  that  of  each 
atom  in  the  molecule  of  a  liquid  compound,  if  it  is  assumed 
that  the  equivalent  of  the  mixture,  or  of  the  molecule,  is  the 
sum  of  the  equivalents  of  the  constituents  of  the  mixture,  or 
of  the  atoms  which  constitute  the  molecule2.  The  'atomic 
refraction'  of  an  element,  deduced  by  each  equation  (i)  to 
(4),  may  be  represented  by  the  symbols  (i)  ra,  (2)  rAt  (3)  ra> 
(4)  rA  respectively. 

1  39.  Is  the  value  of  rA)  or  TA>  constant  for  each  element  in 
all  its  liquid  compounds  ? 

This  question  has  been  considered  by  Gladstone  and  Dale 
(loc.  cit)*,  and  by  Landolt  (loc.  «V.)4,  but  more  especially  by 
Bruhl5. 

Assuming  that  the  refraction-equivalent  of  each  elementary 
atom  has  a  constant  value  in  all  compounds  of  that  element, 
and  that  the  equivalent  of  a  molecule  is  the  sum  of  the 
equivalents  of  the  constituent  atoms,  we  have  the  expression 
for  finding  the  refraction-equivalent  of  a  compound,  OH2^O/>, 


1  Light  with  wave-length  of  the  red  hydrogen  line  Ha  is  usually  employed  for 
determining  /*. 

2  See  Landolt,  Ber.  15.  1033. 

3  See  also,  Gladstone,  C.  S.  Journal.   Trans,  for  1884.  241. 

4  See  also  Pogg.  117.  353.  and  Annalen,  Supplbd.  4.  i. 

5  Ber.  12.  2135  :  13.  1119  and  1520:  14.  2533,  2736  and  2797;  also  (in  more 
detail)  in  Annalen  200.    139:  203.  i,  255,  and  363:  211.  120  (Abstracts  in   C. 
S.  Journal  for  1880.  293  and  781  :  1881.  15  :  1882.  445). 


310  CHEMICAL   STATICS.  [§  139 

and  similarly  for  compounds  of  other  elements.  From  the 
application  of  such  expressions,  Landolt,  and  others,  deduced 
the  following  values ; 

rA  for  H  =  1*29;  for  0  =  271;  forC  =  4'86;  for  8  =  13-53;  for  Cl  =  9'53. 
Or,  if  equation  (4)  [p.  309]  is  employed,  then 

IA  for  H  =  ro2  ;  for  0  =  1*56  ;  for  €=2*43  ;  for  S  =  7'65  ;  for  Cl  =  5'89. 

The  values  oi(RA\  thus  calculated,  for  many  liquid  carbon 
compounds,  were  found  to  agree  with  the  observed  values. 
Thus,  the  refraction-equivalents  of  pairs  of  carbon  compounds 
differing  in  composition  only  by  H2  should  differ  by 
2.  i  '29  =  2*58;  the  following  are  some  of  the  differences  ob- 
served, 

But  the  following  numbers  shew  that  this  generalisation 
does  not  always  hold  good  ; 

Difference  of 

Propylic  alcohol     C3H8O  \ 
Allylic  alcohol        C3H6OX 


0-91 


Propaldehyde         C3H6O\ 
Acraldehyde  C3H4O/ 


/Propylic  chloride  C3H7C1 
°73  \  Allylic  chloride     C3H5C1 


The  refraction-equivalent  of  the  carbon,  hydrogen,  oxygen, 
or  chlorine  atom,  or  of  all  these  atoms,  is  evidently  not  con- 
stant. Now,  if  the  structural  formulae  of  propyl  compounds  are 
compared  with  those  of  allyl  compounds,  it  is  seen  that  in 
the  former  all  the  carbon  atoms  are  represented  as  tetravalent 
(singly-linked),  but  in  the  latter  two  carbon  atoms  are  repre- 
sented as  trivalent  (doubly-linked)  ;  e.g. 

H3=C  —  C  —  C  —  OH        and        H2  =  C  —  C—  C—  OH. 

II       II  I       II 

Jri2     1*2  rd       H2 

Hence,  the  disagreement  between  the  calculated  and  the 
observed  values  of  (R^)  in  the  case  of  allyl  compounds  may  be 
correlated  with  the  presence  of  trivalent  (doubly-linked) 
carbon  atoms  in  the  molecules  of  these  compounds.  More- 
over, the  actual  values  of  (RA)  for  propyl  compounds  agree 


§  139]  APPLICATION   OF  PHYSICAL  METHODS.  31  1 

with  those  calculated  by  the  equation  on  p.  309,  taking  rA  for 
C  =  4-86,  for  H  =  1-29  and  for  O  =  271  ;  but  the  values  found 
for  allyl  compounds  are  about  2  units  greater  than  the  cal- 
culated values.  Thus, 

Difference  between  calculated 
and  observed  (R 

Allyl  alcohol 

„    aldehyde 

„    chloride  2-07  mean  =  2'io. 

Allyl-ethyl  oxide 

„    acetate 

Briihl  has  compared  the  values  of  (RA)  for  a  great  many 
pairs  of  carbon  compounds,  one  series  containing  only  tetra- 
valent,  the  other  also  trivalent  carbon  atoms,  and  has  found 
that  the  observed  agree  with  the  calculated  values  in  the  first 
series,  but  in  the  second  the  observed  values  are  about  2 
units  greater  than  the  calculated  values,  for  each  pair  of  tri- 
valent carbon  atoms  in  the  molecule1. 

This  conclusion  may  be  summarised  by  saying,  that  two 
values  are  to  be  assigned  to  the  refraction-equivalent  of  the 
carbon  atom,  according  as  it  acts  as  a  tetravalent  (singly- 
linked),  or  trivalent  (doubly-linked)  atom.  The  values  are 
these, 

^CIV  =  4'86     :    rACIV=2'43 


Further,  Briihl  has  compared  series  of  compounds  con- 
taining tetravalent  carbon,  and  divalent  oxygen  atoms,  with 
series  containing  tetravalent  carbon,  and  monovalent  (doubly- 
linked)  oxygen  atoms,  and  he  has  found  that  the  value  of  (RA) 
for  any  compound  of  the  second  series  is  about  0*6  greater 
(for  each  monovalent  oxygen  atom)  than  that  for  the  compound 
of  the  first  series  having  the  same  empirical  formula2. 

We  may  then  assign  these  values  to  the  atoms  of  oxygen  : 


Hence  it  would    appear  that  the  influence   exerted   on    the 
refraction-equivalent   of  a  liquid    carbon    compound   by  the 


1  See  numbers  in  Ber.  12.  2142. 

2  See  numbers  in  Ber.  13.  1121. 


312 


CHEMICAL  STATICS. 


atoms  of  carbon  in  the  molecule,  depends  on  whether  each 
carbon  atom  acts  on,  and  is  acted  on  by,  four  or  three  other 
atoms. 

140.  But  does  this  influence  vary  in  accordance  with  the 
nature  of  the  atoms,  between  which  and  the  carbon  atoms 
there  is  direct  mutual  action  ? 

Bruhl1  finds  that  each  of  the  following  groups  of  isomeric 
compounds  of  carbon,  hydrogen,  and  oxygen  has  practically 
the  same  refraction- equivalent. 


I. 
C1H2C  — CH2C1 

and 
C12HC  — CH3 

H2C-CH2-CH3 


II. 


H 


I 
OH 


and 


OH 
H2C-  CH2—  CH, 

Br 

and 


H3C  — C  — C 

I        \H 
H 

and 
H3C  —  C-CH3 


28-6 


26*0 


HC 

I 
Br 


\ 
1      CH 


39-4 


I 
OH 

and 

XCH3 
H9C  — CH 


OH 

/CH3 
C  — CH3 

OH 


and 


HX  —  C  —  C  —  C 

I        I 

H     H 

and 


H3C  — C 


•367 


H      H 

1     1        o 

C       C       C' 

•  \^         \^         \_,  ^ 

I        1            OH 
H      H 
and 

36-3 

1          ^OH 
H 

.  13.  121, 


§  140]  APPLICATION   OF   PHYSICAL  METHODS.  313 

The  molecules  of  the  compounds  placed  in  column  I.  con- 
tain only  tetravalent  carbon,  and  divalent  oxygen  atoms  ; 
those  in  column  II.  contain  both  tetra-  and  tri-valent  carbon, 
and  di-  and  monovalent  oxygen  atoms. 

Briihl  also  finds1  that  although  the  refraction-equivalent 
of  propaldelyde  is  the  same  as  that  of  acetone,  yet  that  of 
the  third  isomeride,  allylic  alcohol,  is  different ;  thus, 

Empirical  formula  C3H6O. 

H  (tf«) 

I  /° 

1.  Propaldehyde  H3C  — C  — C<^  26'o 

I  H 

H 

2.  Acetone  H3C  — C  — CH3  26-0 


3.     Allylic  alcohol  H2C  — C  — C^  27-90 

|          XOH 
H 

A  comparison  of  these  formulae  shews,  that  whereas  in 
isomerides  I  and  2  the  trivalent  carbon  atom  is  in  direct 
union  with  an  oxygen  and  a  carbon  atom,  in  the  third 
isomeride  it  is  directly  bound  only  to  carbon  atoms :  or  we 
may  say  that  isomerides  I  and  2  contain  a  divalent  group 
C — O,  whereas  isomeride  3  contains  a  tetravalent  group  C — C, 
and  a  trivalent  C — O  group. 

If  we  may  draw  a  general  conclusion  from  the  data  con- 
tained in  Bruhl's  paper,  it  would  seem  that  the  value  of  the 
refraction-equivalent  of  a  compound,  CXOVHZ,  is  independent 
of  the  way  in  which  the  interatomic  reactions  are  distributed, 
provided  each  atom  acts  on  its  maximum  number  of  other 
atoms  ;  but  if  this  is  not  so,  then  there  is  a  connection,  not  only 
between  the  valencies  of  the  atoms  in  the  molecule,  but  also 
between  the  distribution  of  the  interatomic  reactions,  and  the 
refraction-equivalent. 

The  latter  part  of  this  statement  is  illustrated  by  the  fact 
that  the  value  of  (RA)  found  for  (CH8)2CO,  and  for  the  acids 

1  loc.  tit. 


314  CHEMICAL   STATICS.  [§  140 

CwH2w+1COOH,  which  all  contain  the  divalent  group  C  —  O, 
agrees  with  that  calculated  on  the  assumption  that 


=4-86  +  3-29 
=  8-15; 

but  nevertheless  the  carbon  atom  in  the  group  C  —  O,  as  this 
occurs  in  the  before-mentioned  molecules,  is  certainly  tri- 
valent. 

On  the  other  hand  the  actual  values  found  for  (RA)  in  the 
molecules  CwH2n_1CH2OH,  CnH2n,  &c.,  where  the  tetravalent 
group  C  —  C  occurs,  agree  with  those  calculated  on  the  as- 
sumption that 

(^xc-cr^^c"1) 
=1172. 

That  there  is  a  distinct  quantitative  connection  between 
the  nature  of  the  polyvalent  atoms  between  which  direct 
action  and  reaction  occurs,  in  unsaturated  molecules,  and  the 
value  of  (RA)  for  these  molecules,  appears  certain  from  the 
results  of  researches  recently  conducted  in  Landolt's  labora- 
tory by  Nasini1. 

Nasini  has  determined  the  values  of  (RA)  and  (RA),  for 
series  of  carbon  compounds  containing  sulphur,  these  com- 
pounds being  divisible  into  two  groups2,  which  may  be 

represented  generally  as 

X' 

(i)     X'  —  S  —  X'          and  (2)     X"—  S. 

X' 

He  gets  the  following  values  for  the  refraction-equivalent  of 
the  sulphur  atom  according  as  it  acts  as  a  divalent  or  as 
a  monovalent  atom, 

r,Sn=  13-53  rAS»=7-65 

^Sr  =  15-09  rASI=8-84. 

1  Ber.  15.  2878. 

2  As  examples  of  compounds  belonging  to  group  (  i  )  may  be  taken,  H5C2  —  S  —  H, 

/S  —  C2H5  /O  —  C,H5 

and   H5C2  —  S—  C2H5;    also  CO  and  CO  ;     and    as    ex- 

\S-C2H5  \S-C2H5 

/S      X0-C2H5 

amples  of  those  belonging  to  group  (2),  C       ,   C  —  S  &c. 

XS      XO  —  C2H5 


§  140]  APPLICATION    OF   PHYSICAL   METHODS.  315 

Wiedemann1  has  also  determined  values  for  r^S,  from  mea- 
surements of  (RA)  of  CO(OEt)2,  CO(OEt)(SEt),  CS(OEt)2, 
CS(OEt)(SEt),  CO(SEt)2,  and  CS(SEt)2.  The  values  agree 
fairly  with  those  found  by  Nasini  ;  they  are  as  follows, 


r^=  14-04 

^8'=  1  6-32  rASJ=9'28. 

But  when  it  is  sought  to  find  values  for  rAS  in  more  com- 
plex compounds  containing  oxygen,  very  different  results  are 
obtained  according  to  the  structure  assigned  to  the  compound 
molecules  in  question.  Thus,  assuming  that  rAOl  =  3*29,  and 
rAQll  =  2"ji,  the  following  results  are  obtained2. 

.0  .0 

(i)  If  S02  =  S<^  I  ,  ^Sn=8'io;  but  if  S02=S/    , 


O 
J, 


/ 
(2)  IfSO3  =  O—  8<J,  r^Sni  =  8'37;  but  if  SO3  =  S  —  O,  ^8™  =  6-63. 


(3)  If  H2S04  =  HO  —  S  —  O  —  OH,  ^Sin  =  8'43. 

O 
O 

I 

(4)  If  H2SO4  =  HO  —  S  —  OH,  r^SIV=7-8s. 

O 

I  think  we  are  justified  in  concluding  that  the  refraction- 
equivalents  of  molecules  containing  polyvalent  atoms,  all,  or 
any,  of  which  act  directly  on  less  than  their  maximum  number 
of  other  atoms,  is  correlated  not  only  with  the  actual  valencies 
of  these  atoms  (i.e.  the  number  of  atoms  between  which  and  each 
polyvalent  atom  there  is  direct  mutual  action),  but  also  with 
the  distribution  of  the  interatomic  actions  (i.e.  the  nature  of 
the  atoms  between  which  there  is  direct  mutual  action)3. 

The  quantity  (RA}  is  conditioned  by  these  factors,  re- 
fractive index  (/A),  density  (d),  and  molecular  weight  (M). 
The  values  of  p  and  d  vary  for  each  compound  :  when  d 
varies  directly  as  //,,  the  value  of  (RA)  remains  constant  for 

1   Wied.  Ann.  17.  577.  2  For  data  see  Nasini  he.  cit. 

3  This  conclusion,  if  accurate,  illustrates  the  justness  of  the  remark  already 
quoted  from  L.  Meyer,  "  what  we  call  double  or  triple  linking  of  atoms  does  not 
consist  of  a  repetition  of  the  process  which  we  call  single  linking." 


316  CHEMICAL  STATICS.  [§  141 

any  number  of  isomerides  ;  but  if  d  varies  in  some  other  ratio 
with  p,  the  value  of  (R^)  is  different  for  each  isomeride.  The 
latter  condition  holds  good  in  such  unsaturated  molecules  as 
have  been  just  defined.  But  in  many  saturated  molecules, 
according  to  Briihl,  the  former  state  of  things  obtains ;  hence, 
although  the  refraction-equivalent  of  such  molecules  is  con- 
stant, yet  their  refractive  indices  vary.  This  conclusion  may 
be  put  in  general  terms  thus.  Isomeric  molecules  containing 
polyvalent  atoms,  all  of  which  act  on  their  maximum  number 
of  other  atoms,  exhibit  equal  refractive  powers  only  when 
their  densities  are  the  same1. 

141.  Values  have  been  assigned  to  the  atomic  refractions 
of  the  elements,  (or  the  refraction-equivalents  of  the  ele- 
mentary atoms).  Assuming  that  these  values  are  justified  by 
the  experimental  data,  it  is  important  to  mark  that  in  making 
use  of  them  we  do  not  assert  that  each  atom  in  a  molecule 
exerts  its  own  refractive  power,  but  rather  that  a  group  of 
certain  atoms  arranged  in  this  or  that  manner,  (as  roughly 
represented  in  the  structural  formula),  exerts  a  definite  refrac- 
tive power,  which  is  increased  or  diminished  by  changes  in 
the  arrangement,  number,  or  nature  of  the  atoms. 

It  would  appear  better  to  assign  values  to  the  refraction- 
equivalents  of  certain  groups  of  atoms,  in  carbon  compounds 
at  least,  rather  than  to  each  individual  atom.  The  following 
table  contains  some  of  these  values,  and  also  recapitulates 
the  '  atomic  refractions '  which  have  already  been  mentioned. 

*A  rA 

CIV  4'86  2-43 

Cm  5-86  3-22 

(C-C)IV  1172  6-44 

(C-0)"  8-15  472 

(CH2)"  7-44  4'47 

O"  271  1-56 

O1  3-29  2-29 

sn  13-53  7-65 

S1  15-09  8-84 

H  1-29  1-02 

Cl  9-53  5-89. 

1  See  Bruhl,  Ber.  13.  1525—26. 


§  142]  APPLICATION  OF   PHYSICAL  METHODS.  317 

142.  The  refraction-equivalents  of  a  few  carbon  com- 
pounds belonging  to  the  benzenoid  group  have  been  deter- 
mined1. The  arrangement  of  carbon  atoms  in  a  closed  chain 
does  not  appear  to  exert  any  special  influence  on  the  values 
of  the  constant  in  question;  thus  (RA)  found  for  benzene,  agrees 
with  that  calculated  on  the  assumption  that  the  six  atoms  of 
carbon  all  act  as  trivalent  atoms  in  the  molecule  C6H6. 

Few,  if  any,  measurements  have  yet  been  made  of  the 
refraction-equivalents  of  carbon  compounds  containing  pairs 
of  divalent  (trebly-linked)  carbon  atoms.  Briihl2  has  deter- 
mined (RJ)  for  a  few  so-called  propargyl  compounds,  derived 
from  the  hydrocarbon  C3H4,  which  possibly  has  the  structure 
H  —  C—  C  —  C=H3. 

Thus, 


found  calculated,  on  the 

Probable  formula.  assumption  that 


Propargylic  alcohol  HC  —  C  —  Cx  24*01  24-45 

XOH 


Propargyl-ethyl  oxide  HC — C  —  C,  39*5°  39'33 

H3C-CH2 


Propargyl  acetate  HC  —  C  —  C\  377  37*33- 

O  —  C—  C 


The  refraction-equivalents  of  some  compounds  containing 
much  carbon,  relatively  to  the  quantities  of  other  elements 
present,  are  considerably  larger  than  the  values  calculated  by 
the  use  of  the  numbers  given  in  par.  141  3. 


1  See  especially  for  data  Landolt,  Ber.  15.  1038  ;  and  Briihl,  Ber.  12.  2142. 

2  loc.  cit.  12.  2146. 

3  For  data  see  Gladstone's  paper,  C.  S.  Journal,  Trans,  for  1884.  241.     See 
also  ante,  par.  138,  footnote  3  (p.  308). 


3l8  CHEMICAL   STATICS.  [§§  143,  144 

143.  We  have  not  yet  sufficient  knowledge  to  enable  us 
to  use   the  refraction-equivalent   of  a   compound,  otherwise 
than   very   tentatively,  as  a  help  in    deciding   between    the 
possible    structural    formulae    assigned    to    that    compound. 
Briihl  has  employed  the  observed  values  of  the  constant  (RA) 
as  an  argument  in  favour  of,  or  against,  certain  formulae,  but 
not,  it  appears  to  me,  with  much  success  \ 

From  comparing  the  values  of  (RA)  with  the  structural 
formulae  of  certain  carbon  compounds,  the  same  naturalist  has 
drawn  conclusions  regarding  the  meanings  of  the  symbolical 
expressions  'single'  and  'double  bonds';  but,  as  seems  always 
the  case  in  attempts  to  deal  with  '  bonds ',  the  foundations  of 
the  reasoning  are  shifting,  and  the  superstructure  is  untrust- 
worthy2. 

144.  If  a  ray  of  plane  polarised  light  is  passed  through 
a  plate  of  quartz  cut  at  right  angles  to  its  optical  axis,  the 
position  of  the  plane  of  polarisation  of  the  emergent  ray  does 
not  coincide  with  that  of  the  incident  ray ;  the  plane  has  been 
rotated  through  a  certain  angle,  called  the  angle  of  rotation. 
If  the  rotation  takes  place  in  the  same  direction  as  that  in 

1  See  Ber.  12.  2146,  and  14.  2736. 

2  See  Book  n.  chap.  iv.  par.  258.     Kanonnikow  (original  paper  in  Russian; 
see  abstract  in  Ber.  16.  3047)  has  found  the  refraction-equivalents   of  a   num- 
ber  of  solid   carbon   compounds,   by   dissolving    them    in    chemically    inactive 
solvents,  and   measuring  the    refractive   indices  of  the  solutions,  the  values  of 
the  indices  of  the  solvent  being  known;    it  is  then  easy  to  find    the   refraction- 
equivalent  of  the  dissolved  substance,   if  it  be  granted  that  the  refraction- equi- 
valent of  a  mixture  is  the  sum  of  the  equivalents  of  its  components  (see  ante, 
p.  307-9).     Kanonnikow  concludes  that  neither  the  degree  of  concentration  of  the 
solution,   nor  the  physical  condition  of  the  solid,  exerts  any  marked  effect  on 
the  refractive  power  of  the  dissolved  substance. 

Conclusions  are  drawn  as  to  the  structural  formulae  of  various  carbon  com- 
pounds ;  Briihl's  generalisations,  on  the  whole,  are  confirmed. 

The  same  chemist  (see  abstract  in  Ber.  17.  ref.  157.  [the  abstracts,  referate,  in 
the  Berichte  beginning  with  vol.  1 7  are  paged  separately  from  the  original  papers]) 
has  attempted  to  determine  rA  for  various  metals,  by  finding  (RA)  for  various 
salts  of  carbon  acids,  and  deducting  (RA)  for  the  acids.  His  numbers  point  to 
the  conclusion  that  in  a  '  group  '  of  metals  (as  '  group  '  is  used  in  the  classification 
based  on  the  periodic  law),  rA  increases  as  the  atomic  weights  of  the  metals 
increase.  Kanonnikow  also  tries  to  deduce  values  for  (RA]  for  the  groups  NO3, 
SO4,  &c.,  and  so  to  find  the  distribution  of  the  interatomic  actions  in  sulphates, 
nitrates,  &c. 


§  144]  APPLICATION   OF   PHYSICAL   METHODS.  319 

which  the  hands  of  a  watch  appear  to  move  as  we  look  at 
the  face,  the  quartz  is  said  to  exhibit  dextrorotatory  power ; 
this  is  expressed  by  prefixing  +  to  the  value  of  the  angle  of 
rotation.  If  the  rotation  takes  place  in  the  direction  opposite 
to  that  in  which  the  hands  of  a  watch  appear  to  move  as  we 
look  at  the  face,  the  quartz  is  said  to  exhibit  laevorotatory 
power;  this  is  expressed  by  prefixing  -  to  the  value  of  the 
angle  of  rotation. 

Optically  active  transparent  media  are  those  which  rotate 
the  plane  of  polarisation  of  a  ray  of  light  passed  through 
them  ;  they  are  divided  into  dextrorotatory  substances,  e.g. 
some  specimens  of  quartz,  sugar  in  aqueous  solution,  &c.,  and 
laevorotatory  substances,  e.g.  other  specimens  of  quartz,  tur- 
pentine, quinine  in  alcoholic  solution1,  &c. 

To  determine  the  amount  of  rotation  caused  by  any  sub- 
stance, it  is  necessary  to  have  an  instrument  wherein  a  ray  of 
light  may  be  polarised,  and  the  position  of  the  plane  deter- 
mined; the  polarised  ray  may  be  passed  through  a  known 
quantity  of  the  medium  under  examination ;  and  finally  the 
position  of  the  plane  of  the  emergent  ray  may  be  deter- 
mined. Such  instruments,  known  as  polarimeters  or  polaristro- 
bometers,  are  described  in  detail  in  various  text-books2. 

Let  us  consider  a  liquid  carbon  compound,  say  C10H16. 
The  angle  of  rotation,  ot,  depends  on  (i)  the  thickness  of  the 
layer  of  liquid  through  which  the  light  passes,  (2)  the  wave- 
length of  the  ray  of  light  employed3,  and  in  most  cases, 
(3)  the  temperature  at  which  the  observation  is  made.  The 
first  of  these  conditions  will  be  determined  if  we  know  the 


1  For  details  concerning  polarised  light,  and  circular  polarisation  considered 
from    the    physical   stand-point,    see    Glazeb rook's   Physical   Optics,    chaps.    XI. 
and  xiv. 

2  See    especially    Armstrong   and    Groves,    Organic  Chemistry,  569  et  seq. ; 
and  also  Watts's  Dictionary,  3rd  Supplt.  1198 — 1207. 

3  The  angle  of  rotation,  a,  was  supposed  by  Biot  to  vary  inversely  as  the  square 
of  the  wave-length  of  the  light  employed,  but  Boltzmann  has  shewn  that  the 

/?  /°* 

expression  a  =  ^  +  \A>  where  B  and  C  are  constants  determined  experimentally,  is 

a  nearer  approximation  to  the  law  :  but  the  values  of  B  and  C  appear  to  differ 
slightly  for  different  media.     See  Watts's  Diet.  3rd  Supplt.  1207. 


320  CHEMICAL  STATICS.  [§  144 

length  of  the  column  of  liquid  employed,  and  the  second  is 
rendered  definite  by  making  use  of  monochromatic  light. 

Let  /  =  length  of  column  of  liquid  in  decimetres,  d—  density 
of  liquid  referred  to  water  at  4°,  and  a  =  angle  of  rotation  of 
plane  of  polarisation  of  light  of  given  wave-length  ;  then 

[a]  =  specific  rotatory  power  of  the  liquid,  for  the  given  ray,  =  -j—/' 

That  is  to  say,  the  specific  rotatory  power  of  an  optically 
active  substance  is  the  angle  through  which  the  plane  of 
polarisation  of  a  given  ray  is  rotated  by  passing  through  a 
column  i  decimetre  long  of  a  liquid  containing  I  gram  of  the 
substance  in  I  cubic  centimetre.  If  the  substance  to  be  ex- 
amined is  a  solid,  it  must  be  dissolved  in  an  optically 
inactive  menstruum.  In  such  a  case,  let  /=  length  in  deci- 
metres of  column  of  solution  employed,  /  =  grams  of  opti- 
cally active  substance  in  100  grams  of  solution  (i.e.  gram- 
percentage  composition),  and  d=  density  of  solution  referred 
to  water  at  4°;  then  /.  d=  c  =  concentration,  i.e.  grams  of 
active  substance  in  100  c.c.  of  solution. 

r  .,       100  a        100  a 

Hence  [a]=7^rT7- 

As  the  value  of  [a]  generally  rises  as  temperature  rises l, 
thermometric  observations  must  be  made.  The  value  of  [a] 
also  varies  with  variations  in  (i)  the  nature,  and  (2)  the  quan- 
tity, of  inactive  solvent  employed  ;  the  preceding  formula 
therefore  gives  only  the  apparent  specific  rotatory  power  of 
the  solid  substance. 

That  [a]  varies  according  to  the  nature  of  the  solvent,  is 
shewn  by  Hesse's  observations  on  turpentine  oil2; 

pure  turpentine  oil + alcohol  oil + benzene  oil+ acetic  acid 

(QoHie)  (amount  of  solvent  varied  in  each  case  from  10  per  cent,  to  90  per  cent.) 

HD       37°'oi ;     37°'035  to  38°'486;  37°'i94  to  39°'449 ;  37°'i48  to  4o0>222. 

1  For  numbers  illustrative  of  this  in  the  case  of  aqueous  solutions  of  tartaric 
acid  see  Diet.,  3rd  Supplt.  1209. 

2  Hesse,  Annalen  176.  89  and  189  :  see  also  Landolt's  Handbook  of  the  Polari- 
scope  (English  translation),   54 — 94.     This  book  presents  a  very  complete  view 
of  the  whole  subject  of  circular  polarisation,  chemically  considered. 


§  144]  APPLICATION  OF  PHYSICAL  METHODS.  321 

The  following  numbers *  illustrate  the  dependence  of  [a] 
on  the  amount  of  solvent  employed  ; 

Value  of  [a]D 

Difference 


Aqueous  solution  of 

maximum 

minimum 

Tartaric  acid 

+   I4°'i8 

+       3°-20 

Codeine 

-137*75 

-iii°'5o 

Quinine 

-i69°-25 

-ii6°'o 

Landolt  (loc.  tit.}  has  shewn  that  the  true  value  of  [a] 
may  generally  be  found  from  a  number  of  observations  made 
with  solutions  of  varying  concentration  ;  the  more  con- 
centrated the  solution  the  more  nearly  does  the  value  found 
for  [a]  approach  the  true  value,  i.e.  the  more  nearly  does  the 
observed,  agree  with  the  true  specific  rotatory  power.  It 
is  better  to  use  several  solvents,  and  make  a  series  of  observa- 
tions with  each  ;  the  value  deduced  for  [a]  is  generally  the 
same  for  each  solvent. 

The  nature  and  extent  of  the  variations  in  [a]  caused  by 
varying  the  quantity  of  solvent  appear  to  differ  for  each 
optically  active  solid  substance2;  in  some  cases  the  relation  is 
very  complicated,  in  others  it  may  be  expressed  by  a  compa- 
ratively simple  formula8. 

That  the  observed   and   calculated  values   of  [a]   agree 

1  Landolt,  loc.  cit. 

2  The  following  numbers  illustrate  this  statement  (Landolt,  loc.  cit.  82): 


Active  substance. 

Solvent. 

[O]D  for 
pure  substance. 

[<X]B  for 
maximum 
dilution. 

Difference. 

Isevorotatory  turpentine 

alcohol 

360-97 

38079 

+    I°'82 

dextrorotatory         ,, 

» 

140-17 

i5°'35 

+    I°'l8 

laevorotatory  nicotine  

(alcohol 
(water 

i6i°'29 

74°'i3 

-22°'24 
-870-16 

dextrorotatory  ethyl  tartrate 

falcohol 
[water 

8°'27 
8°  -09 

io°'i9 

28°'I2 

+     I°'92 
+  20°  -03 

3  Thus,  for  solutions  of  turpentine  in  alcohol,  Landolt  gets  the  formula 
[a]/>  =  36°'974  +  '0048164?  +  -oooi  33  1?2 

where  q  —  percentage    of  inactive   solvent.     (For  more  details  see  Landolt,  loc. 
dt.  8  r  —  94.) 

For  a  fuller  treatment  of  the  methods  employed  for  rinding  the  true  value  of 
[a]  from  observations  on  solutions,  see  Diet.  3rd  Supplt.  1212  —  1213. 

M.  C.  21 


322  CHEMICAL  STATICS.  [§  145 

closely,  provided  a  sufficient  number  of  observations  is  made, 
is  evident  from  these  results  (Landolt). 

|_fl_|0  calculated  from  observations  on  mixtures  with 

Active  substance        [a]D  observed        (i)  (2)  (3)  (4)  (5)      max.  diff. 

C2H5OH    CH3OH      H20         C6H6     CH3CO2H 

Dextrorotatory)  _0              00            00          00 

ethyl  tartrate}  8  3'        S '27      8 '42    8  ^ 

Dextrorotatoryj  _        _          _          _ 

turpentine     / 

Lfevorotatory   )  ,„ 

turpentine     }  37 '°'       *  '97                            *  '97    *  ^      ~'12 

Lsevorotatory   }  ,  „  0 

J    Y     161  '55     160 '83        —     ioi  -29      —  -72 

nicotine       ) 

The  true  specific  rotatory  powers  of  camphor,  cane  sugar, 
and  dextroglucose  have  been  determined  by  Landolt,  Tollens, 
and  Schmitz1.  But  I  think  it  should  be  noted  that  the  obser- 
vations on  which  the  method  for  determining  [a]  is  based, 
were  necessarily  made  with  solutions  of  liquid  compounds  in 
inactive  solvents,  whereas  in  the  cases  of  camphor  and  sugar 
we  have  to  deal  with  solutions  of  solid  substances  ;  it  is  possible 
that  the  value  of  [a]  for  liquid  camphor  may  vary  very  much 
from  that  for  solid  camphor2.  It  should  also  be  observed  that 
any  deductions  concerning  the  relations  between  specific 
rotatory  power  and  molecular  structure,  drawn  from  a  study 
of  liquid  compounds,  could  not  be  applied  in  a  precise  manner 
to  solid  compounds,  assuming  the  true  value  of  [a]  for  these 
compounds  to  be  known. 

145.  In  attempting  to  trace  the  relations  which  un- 
doubtedly exist  between  the  specific  rotatory  power  and  the 
structure  of  compounds,  we  must  distinguish  relationships 
between  this  constant  and  the  composition  of  molecules  whose 
empirical  formulae  at  least  are  known,  from  those  between 
the  same  constant  and  such  mixtures  of  molecules  in  varying 
proportions  as  are  presented  by  solutions  of  known  con- 
centration. 

1  See  Landolt,   loc.    cit.   84 — 92:    Tollens,   and   Schmitz   in   Ber.   9.   1531: 
10.  1403:  and  do.  1414. 

2  Biot  states  that  fused  liquid  tartaric  acid  is  markedly  dextrorotatory,  but  the 
solidified  acid  is  feebly  Isevorotary  (Diet.  3rd  Supplt.  1209).     Landolt's  value  of 
[a]  for  solid  camphor  is  55°'6  (see  Diet.,  loc.  cit.  374)  :  while  Gernez  obtained 
the  value  7o°*33  for  fused  camphor  (do.  do.  p.  1209). 


§  146]  APPLICATION  OF  PHYSICAL  METHODS.  323 

For  although  in  the  latter  cases  no  precise  conclusions  can 
be  drawn  regarding  the  relative  arrangements  of  the  atoms  in 
the  molecules,  yet  the  study  of  specific  rotatory  power  may 
help  to  throw  light  on  such  general  questions  as  the  action  of 
solvents,  the  distinction  between  chemical  and  physical  change, 
and  so  forth. 

146.  Most  of  the  known  compounds  which  possess  the 
power  of  rotating  the  plane  of  polarisation  of  a  ray  of  light 
contain  carbon  :  van't  Hoff,  following  in  the  steps  of  Le  Bel, 
has  endeavoured  to  trace  a  precise  connection  between  the 
molecular  structure  of  these  compounds  and  their  rotatory 
power.  The  molecule  of  every  optically  active  compound, 
according  to  this  hypothesis,  contains  one  or  more  asymmetric 
atoms  of  carbon.  The  conception  represented  by  this  expres- 
sion is  essentially  crystallographic. 

An  asymmetric  atom  of  carbon  directly  acts  on,  and  is  acted 
on  by,  four,  chemically  different,  monovalent  atoms,  or  groups 
of  atoms,  within  the  molecule  ;  —  thus 


R3-C-R2 
R4 

To  render  the  conception  more  definite,  the  carbon  atom  is 
supposed  to  be  situated  at  the  centre  of  a  tetrahedron  and 
each  monovalent  radicle  at  one  of  the  summits.  Inasmuch  as 
these  radicles  are  chemically  different,  the  action  and  reaction 
between  each  and  the  carbon  atom  is  supposed  to  be  differ- 
ent; hence  each  radicle  is  situated  at  a  different  distance 
from  the  central  atom  of  carbon  ;  and  hence  the  tetrahedron 
is  irregular,  has  no  planes  of  symmetry,  and  is  capable  of 
existing  in  non-superposable  (enantiomorphous]  forms.  Optical 
activity  is  regarded  as  always  accompanied  by  such  an  ar- 
rangement as  this  of  atoms  in  molecules,  which  molecules 
have  thus  the  properties  of  partially  developed  non-superpos- 
able crystals1. 

1  For   a  more  detailed    account    of  van't   Hoff's  hypothesis,  see  Diet.  3rd 
Supplt.  1214—1217  ;  or  Armstrong  and  Groves,  loc.  cit.  986—993. 

21—2 


324  CHEMICAL  STATICS.  [§  146 

Representing  the  asymmetric  carbon  atom  (or  atoms)  in  a 
molecule  by  an  italicised  C,  we  have  such  formulae  as  these ; 

OH  H2  OH 

I  II        I 

Lactic  acid,  H3C  —  C—  CO2H  ;      Malic  acid,  HO2C  —  C  —  C  —  CO2H  ; 

H  H 

OH  OH  OH  OH 

I        I        I 

Mannitol,  HOH2C—  C—  C—  C  —  C—  CH2OH. 
I        I        I        I 
H      H      H      H 

Any  compound,  the  molecule  of  which  contains  a  single 
asymmetric  carbon  atom,  may  exist  in  two  optically  different 
modifications.  When  more  than  one  asymmetric  atom  is 
present,  the  number  of  possible  modifications  is  conditioned  by 
whether  the  formula  of  the  compound  is  symmetrical  or  un- 
symmetrical:  a  symmetrical  formula,  in  the  nomenclature  of 
this  hypothesis,  is  one  in  which  the  radicles  directly  connected 
with  the  different  asymmetric  carbon  atoms  are  the  same ; 
if  these  radicles,  or  some  of  them,  are  different,  the  formula 
is  said  to  be  unsymmetricaL  Thus  the  formula 

(R3R2R1)C-C(R1R2R3), 
or 


I     I 

(R4R5)C-C(R4R5) 
is  symmetrical :  but  the  formula 

(R^Ri)  C  —  C  (R4R5R6),       or       (R2nR2nC)  — 

is  unsymmetricaL 

A  carbon  compound  of  unsymmetrical  formula,  containing 
n  asymmetric  atoms  of  carbon,  may  exist  in  (2)"  modifications ; 
if  the  compound  is  represented  by  a  symmetrical  formula,  it 

n 

n       (2Y  —  (2]z 

may  exist  in  (2)  -  +  ~ —  forms1.     Thus  tartaric  acid  is 

represented  by  the  formula 

1  See    illustrations    of   these  equations  in  Diet.   3rd   Supplt.    1138 — 39;  or 
Armstrong  and  Groves,  loc.  dt.  987 — 990. 


§  146]  APPLICATION   OF   PHYSICAL  METHODS.  32$ 

OH  OH 

I         I 
H02C  —  C—  C—  C02H, 

H      H 

which  is  symmetrical,  and  contains  two  asymmetric  atoms 
of  carbon.  The  van't  Hoff  hypothesis  asserts  the  possible 
existence  of  three  optically  different  tartaric  acids,  which  may 
be  represented  by  the  symbols 

(i)  +A+A(=2A),       (2)  +A-A(=o\       (3)   -A-A  =  (2[-AD; 

where  each  part  of  the  symmetrical  molecule, 

OH 

I 
i.e.  each  HO2C  —  C 

H 

is  represented  by  the  sign  A  ;  the  symbol  +  or  —  being  pre- 
fixed according  as  this  group  is  regarded  as  being  dextro-  or 
laevorotatory.  One  of  the  hypothetically  possible  tartaric  acids 
ought  therefore  to  be  dextro-  and  one  laevorotatory ;  the 
third  ought  to  be  inactive,  because  of  the  balance  of  dextro- 
and  laevorotatory  powers  within  the  molecule.  Now  three 
such  acids  exist1. 

When  a  substance  is  regarded  as  being  inactive  because 
of  the  balance  of  opposite  rotatory  powers  by  the  struc- 
ture of  the  molecule  itself,  it  is  said  to  be  inactive  by  in- 
ternal compensation.  But  a  substance  may  also  be  inactive 
by  external  compensation.  Thus  erythritol  is  probably  repre- 
sented by  the  symmetrical  formula  containing  a  pair  of  asym- 
metric carbon  atoms 

OH  OH 

I        I 
HOH2C—  C—  C  —  CH2OH. 

H      H 
This  substance  is  said   to   be  optically  inactive  because  of 

1  Racemic  acid  is  probably  a  molecular  compound  of  the  dextro-  and  Izevo- 
rotatory  acids. 


326  CHEMICAL  STATICS.  [§  146 

internal  compensation.  But  by  distillation  with  formic  acid 
erythritol  yields  the  glycol 

OH 

HOH2C—  C  —  C  —  CH2. 
H     H 

This  glycol,  although  containing  one  asymmetric  carbon  atom, 
is  inactive.  But  the  hypothesis  asserts  that  two  optically 
different  modifications  of  this  glycol  may  exist :  if  we  suppose 
that  both  are  actually  produced,  and  produced  in  equal  mole- 
cular quantities,  we  have  an  explanation  of  the  non-activity  of 
the  glycol ;  it  is  inactive  by  external  compensation. 

This  explanation  appears  to  me  to  require  that  we  regard 
the  glycol  in  question  as  owing  its  optical  inactivity  to  the 
existence  of  molecular  groups,  each  composed  of  two  chemi- 
cally identical  but  optically  dissimilar  molecules:  it  could 
scarcely  be  that  a  mixtiire  of  the  dextro-  and  laevorota- 
tory  molecules  would  always  give  an  inactive  substance 
which  could  not  be  separated  into  its  optically  different 
parts. 

Many  carbon  compounds  said  to  contain  asymmetric  carbon 
atoms  are  optically  inactive.  This  does  not  seem  to  me  to  be 
a  material  objection  to  the  van't  Hoff  hypothesis.  Because 
when  we  speak  of  an  asymmetric  carbon  atom,  we  mean  more 
than  is  symbolised  by  the  expression  CRJR.JR3R4 ;  we  mean 
not  only  that  the  carbon  atom  is  in  direct  union  with  four 
chemically  unlike  monovalent  radicles,  but  also  that  the 
structure  of  this  group,  CR^R^,  is  of  a  special  kind,  and  of 
a  kind  which,  by  the  very  terms  of  the  hypothesis,  cannot  be 
distinguished  from  other  possible  structures  by  any  chemical 
methods  we  at  present  possess.  Whether  a  structure 
CR^RgR.i  shall  or  shall  not  be  associated  with  optical 
activity,  depends  (by  hypothesis)  on  the  relative  arrangement 
in  space  of  the  five  parts  which  compose  the  structure ;  but 
this  again  depends  on  the  equality  or  non-equality  of  the 
mutual  actions  between  C  and  R1?  C  and  R2,  C  and  R3,  and 
C  and  R4;  and  this,  finally,  depends  on  the  chemical  nature  of 


§  146]  APPLICATION   OF   PHYSICAL   METHODS.  327 

Rj,  R2,  R3  and  R4,  using  the  expression  chemical  nature  in 
its  widest  acceptation1. 

We  may  object  to  the  extremely  crystallographic  character 
of  the  van't  Hoff  hypothesis,  and  to  the  length  to  which 
it  pushes  the  vague  notion  of  *  bonds '  or  '  units  of  affinity ', 
for  it  seems  to  regard  these  as  capable  of  definite  arrangement 
in  space ;  but  I  think  the  hypothesis  is  worthy  of  careful  con- 
sideration, because  it  draws  attention  to  the  inadequacy  of 
the  prevalent  conceptions  regarding  isomerism  and  molecular 
structure,  and  because  it  bases  the  explanation  it  has  to  give 
of  the  connection  between  such  structure  and  the  properties  of 
compounds  on  essentially  dynamical  conceptions. 

But  can  it  be  shewn  that  optical  activity  is  undoubtedly 
connected  with  the  structure  of  the  molecules  of  compounds, 
rather  than  with  that  of  groups  of  molecules  ? 

It  is  said2  that  the  specific  rotatory  power  of  terpene 
(Ci0H16)  from  French  turpentine  oil,  and  of  camphor  (C10H16O), 
is  independent  of  temperature,  and  is  indeed  the  same  for 
these  substances  in  the  gaseous  as  in  the  liquid  state :  if  this 
is  confirmed  by  further  observations  we  shall  have  in  these 
compounds  instances  of  undoubted  connection  between  mole- 
cular structure  and  rotatory  power.  But  the  great  majority  of 
optically  active  carbon  compounds  do  not  certainly  exhibit 
such  a  connection,  or  exhibit  it  only  in  an  indirect  manner. 
Thus  it  cannot  be  asserted  that  the  molecule  of  lactic  acid 
(CH3  — CHOH  —  CO2H)  is  optically  active,  because  no  one 
has  yet  obtained  molecules  of  this  acid  unmixed  with  mole- 
cules of  other  substances.  Again,  we  do  not  know  the  true 
molecular  weights  of  tartaric  or  malic  acids  :  even  in  the  cases 
of  amylic  alcohol,  and  valeric  acid,  which  are  gasifiable  com- 
pounds, we  cannot  assert  that  the  molecule  C4H9.  CH2OH,  or 
the  molecule  C4H9.  CO2H,  is  optically  active,  because  the  opti- 
cal activity  of  the  compounds  in  question  belongs  to  them  in 

1  For  a  tabular  statement  of  compounds,  shewing  in  what  cases  the  presence  o^ 
the  structure  symbolised  by  CR1R2R8R4  is  accompanied  by  optical  activity,  see 
Landolt,  loc.  cit.  27 — 9 ;  see  also  table,  loc.  cit.  p.  36.     Just.  Annalen  220.  146  has 
shewn  that  a  number  of  derivatives  of  active  amylic  alcohol  are  themselves  optically 
active. 

2  See  Diet.  3rd  Supplt.  1209. 


328  CHEMICAL  STATICS.  [§  147 

the  liquid,  not  in  the  gaseous,  state.  Moreover  optically  active 
amylic  alcohol,  or  valeric  acid,  is  easily  changed  by  the  action 
of  heat  into  the  inactive  modification,  and  this  change  is  said 
to  be  unaccompanied  by  any  change  in  purely  chemical 
reactions.  Again,  tartaric  acid  is  supposed  by  the  van't  Hoff 
hypothesis  to  be  active  because  of  the  structure  of  the  mole- 
cule CO2H  -  (CHOH)2  -  CO2H  ;  but  the  connection  between 
the  refrangibility  of  the  light  employed,  and  the  observed 
values  of  [a]  for  an  aqueous  solution  of  the  dextrorotatory 
acid,  of  varying  concentration,  shews  that  this  solution  very 
probably  contains  a  compound  of  the  acid  and  water,  of  oppo- 
site optical  power  to  that  of  the  acid1.  In  other  words  mere 
solution  in  water  has  apparently  sufficed  to  change  the  struc- 
ture of  the  molecule  of  tartaric  acid. 

The  great  readiness  with  which  the  value  of  [a]  undergoes 
change  when  the  compound  exhibiting  rotatory  power  is 
subjected  to  small  physical  changes,  or  is  brought  into  contact 
with  other  compounds,  appears  to  shew  that  in  most  cases  at 
any  rate,  the  power  of  rotating  the  polarised  ray  is  to  be 
regarded  as  a  property  rather  of  groups  of  molecules,  than  of 
the  groups  of  atoms  which  form  these  molecules.  But  the 
power  of  forming  groups  characterised  by  such  a  marked 
property  as  optical  activity,  must  be  connected  with  the  nature 
of  the  molecules  which  form  these  groups.  We  have  seen  that 
the  nature  of  a  molecule  depends  on  the  nature,  number,  and 
relative  arrangement  of  its  atoms :  hence,  in  an  indirect  sense, 
optical  activity  is,  on  this  view  of  the  matter,  to  be  associated 
with  the  structure  of  molecules. 

147.  Numbers  have  already  been  given  shewing  that  the 
values  of  [a],  determined  for  solutions  of  optically  active  com- 
pounds, vary  in  accordance  with  the  nature  and  relative 
quantities  of  the  solvents  employed.  A  more  detailed  study 
of  the  connections  between  these  constants  serves  to  emphasise 
the  dependence  of  rotatory  power  on  the  existence  of  groups 
of  molecules. 

Krecke2  has  attempted  to  generalise  the  relations  between 

1  See  Diet.  3rd  Supplt.  1207—8. 

2  Journal  fur prakt.  Chemie  (2)  5.  6  :  see  also  Flavitsky,  Ber.  15.  5. 


§  147]  APPLICATION  OF  PHYSICAL  METHODS.  329 

the  value  of  [a]  for  a  given  compound,  and  for  substances 
derived  from  it  by  the  action  of  inactive  solvents  or  chemical 
reagents :  in  these  cases  it  is  asserted  that  the  so-called  mole- 
cular rotatory  power,  i.e.  ([a] .  M\  either  remains  unaltered,  or  is 
increased  to  a  simple  multiple  of  that  of  the  original  substance. 
But  when  we  remember  that  the  value  of  ([a]  .  M )  is  known  for 
very  few  compounds,  we  see  that  the  means  are  wanting  for 
proving  or  disproving  the  statement  made  by  Krecke. 

It  seems  at  present  impossible  to  foretel  whether  the 
optical  activity  of  a  compound  will  be  altered  or  not,  and  if 
altered,  in  what  direction  the  change  will  proceed,  when  the 
compound  is  mixed  with  optically  inactive  solvents.  Thus, 
the  rotatory  power  of  an  aqueous  solution  of  tartaric  acid  is 
increased  by  addition  of  boric  acid,  but  decreased  by  addition 
of  hydrochloric  or  sulphuric  acid.  A  solution  of  tartaric 
acid  in  absolute  methylic  alcohol  is  said  to  be  inactive1,  but 
a  feebly  laevorotatory  solution  of  the  same  acid  in  acetone 
becomes  dextrorotatory  on  addition  of  a  little  water. 

Further,  the  simultaneous  presence  of  two  inactive  solvents 
sometimes  produces  effects  that  would  not  be  expected  from 
the  action  of  either  separately.  About  one-half  of  the  alcohol 
in  an  alcoholic  solution  of  cinchonine  may  be  replaced  by 
chloroform  without  much  alteration  of  rotatory  power,  but  if 
as  much  as  ¥ i_th  of  the  chloroform  in  a  solution  of  the  same 
alkaloid  in  this  solvent  is  replaced  by  alcohol  a  marked 
change  in  rotatory  power  occurs2. 

It  seems  probable  that  in  at  least  the  majority  of  cases 
where  the  rotatory  power  is  considerably  modified  by  addition 
of  optically  inactive  bodies,  this  modification  is  to  be  con- 
nected with  the  formation  of  more  or  less  unstable  groups  of 
molecules,  and  so  with  the  production  of  a  liquid  in  which 
groups  of  different  degrees  of  complexity  are  simultaneously 
present3.  Instructive  illustrations  of  the  modification  in 
question  are  presented  by  milk  sugar  and  by  the  glucoses 

1  Landolt,  Ber.  6.  1078. 

2  Diet.  3rd  Supplt.  1210. 

3  For  details  concerning  modification  of  rotatory  power  by  action  of  solvents 
or  reagents,  see  Landolt,  loc.  cit.  35 — 41. 


33O  CHEMICAL  STATICS.  [§  147 

C6H12O6 .  H2O.  When  a  freshly  prepared  aqueous  solution  of 
one  of  these  substances  is  kept  at  a  given  temperature  for 
some  time,  the  value  of  [a]  gradually  decreases  until  a  certain 
limit  is  reached.  The  final  value  is  more  quickly  attained  by 
boiling  the  solution ;  on  the  other  hand  cold  decreases  the 
rate  at  which  the  value  of  [a]  diminishes.  Thus, 

Value  of  [a]D 

immediately  after  preparation  after  rotation  has  become 

of  solution  constant 

Dextrorotatory  milk  sugar  80° '68  5 3° '63 

„  honey  sugar  9i°*o  46°'58 

Now  each  of  these  sugars  exists  in  a  crystalline  and  in  an 
amorphous  form,  the  latter  being  produced  from  the  former  by 
fusion.  As  a  solution  in  water  of  the  amorphous  form  has 
a  constant  rotatory  power,  equal  to  the  smallest  value  found 
for  a  solution  of  the  corresponding  crystalline  form,  it  is 
concluded  that  the  latter  solution,  when  freshly  prepared, 
contains  groups  of  molecules  of  different  complexity,  of  which 
some,  and  these  the  least  stable  groups,  exhibit  a  much  higher 
rotatory  power  than  others1. 

The  facts  known  concerning  optically  active  crystalline 
solids  are  on  the  whole  in  keeping  with  the  view  that  the 
rotatory  power  of  these  substances  is  connected  with  the 
existence  of  more  or  less  complex  groups  of  molecules.  All 
substances  known  to  be  optically  active  in  the  state  of  crystal- 
line solids,  with  the  exception  of  two2,  lose  their  rotatory 
power  when  liquefied  by  fusion  or  when  dissolved.  These 
substances  all  crystallise  in  partially  developed  non-super- 
posable  forms.  Inasmuch  as  they  are  inactive  when  the 
crystalline  structure  is  destroyed,  there  must  be  an  intimate 
connection  between  the  power  they  possess  of  rotating  a 
polarised  ray,  and  the  arrangement  of  the  particles  which 
compose  their  crystals. 

Pasteur  supposed  that  the  smallest  crystalline  particle  of 
one  of  these  substances  is  composed  of  molecules  arranged  in 
right-  and  left-handed  spirals,  each  spiral  being  non-super- 

1  Landolt,  he.  tit.  62. 

2  These  exceptions  are  Strychnine  sulphate  and  Amylamine  alum. 


§  148]  APPLICATION   OF   PHYSICAL  METHODS.  331 

posable  on  the  other,  and  that  when  the  crystals  are  liquefied 
by  fusion,  or  are  dissolved,  this  peculiar  structure  is  destroyed, 
and  with  it  the  power  of  rotating  a  polarised  ray  is  removed. 
This  hypothesis  has  been  so  far  confirmed  by  Sohncke,  who 
has  arranged  thin  plates  of  mica  to  represent  Pasteur's  spiral 
groups  of  molecules,  and  has  thus  obtained  an  optically  active 
substance1. 

148.  Researches  on  the  relations  between  the  composition 
and  the  absorption-spectra  of  carbon  compounds  have  been 
conducted  by  Hartley2.  This  chemist  has  shewn  that  the 
normal  alcohols,  CnH2n+1  OH,  do  not  absorb  any  of  the  ultra- 
violet rays;  that  the  normal  acids,  CBH8B+1 CO2H,  cause  a 
slight  absorption  of  these  rays,  the  intensity  of  the  absorption 
increasing  as  the  molecular  weight  of  the  acid  increases  ;  and 
that  benzene  and  its  derivatives  exhibit  strong  absorption, 
and  are  characterised  by  the  appearance  of  absorption-bands, 
the  position  of  which  can  be  determined  when  a  transparent 
diluent  is  added. 

From  an  examination  of  the  absorption-spectra  of  very 
many  carbon  compounds,  Hartley  concludes,  that  absorption- 
bands  are  never  present  in  the  ultra-violet  part  of  the  spec- 
trum obtained  by  passing  light  through  a  compound  in  the 
molecule  of  which  the  carbon  atoms  are  arranged  in  an  '  open 
chain',  but  that  such  bands  are  present  in  the  absorption- 
spectra  of  all  benzene  derivatives.  Inasmuch,  however,  as 
benzene  hexchloride  C6H6C16  is  very  transparent,  and  exhibits 
no  bands,  it  would  appear  that  the  mere  closing  of  the  chain 
of  carbon  atoms  is  not  the  sole  condition  necessary  for  the 
production  of  absorption-bands.  Hartley  thinks  that  each 
carbon  atom  must  be  in  direct  union  with  at  least  three  other 
carbon  atoms. 

This  supposition  is  in  accordance  with  the  observation, 
that  solutions  of  naphthalene,  anthracene,  and  phenanthrene, 
in  transparent  media,  shew  absorption-bands,  similar  to,  but 

1  For  details  see  Landolt,  loc.  cit.  19 — 20  :  or  Diet.  3rd  Supplt.  1214. 

2  Phil.  Trans.  170.  257.     See  also  C.  S.  Journal  Trans,  for  1881.  153  et  seq. 
See  also  report  of  the  B.A.  committee  on  Spectrum  Analysis ;  Brit.  Ass.  Reports 
for  1880.  258  et  seq. 


332  CHEMICAL  STATICS.  [§  148 

lower  in  refrangibility  than,  the  benzene  bands ;  and  that 
these  solutions  likewise  exhibit  much  more  intense  absorption 
than  benzene. 

Terpenes  (C10H16)  and  camphor  (C10H16O)  exhibit  more 
intense  absorption  than  compounds  of  the  paraffinoid  group, 
but  no  bands  appear  in  the  spectra  of  the  light  transmitted 
by  these  compounds ;  hence  their  molecular  structure  appears 
to  be  related  on  the  one  hand  to  the  paraffinoid  and  on  the 
other  to  the  benzenoid  group  of  compounds. 

By  taking  advantage  of  the  differences  in  the  character  of 
the  absorption  exhibited  by  different  compounds, — e.g.  the 
character  of  the  absorption-spectrum  of  cymene  is  very  dif- 
ferent from  that  of  the  terpenes, — it  is  possible  to  detect 
minute  quantities  of  certain  compounds  in  presence  of  large 
quantities  of  others,  and  also  broadly  to  classify  carbon 
compounds  into  groups.  Further,  by  taking  advantage  of 
the  differences  in  the  positions  of  the  bands  in  the  spectra  of 
the  light  transmitted  by  isomeric  compounds,  it  will  be 
possible,  when  sufficient  data  have  been  obtained,  to  de- 
termine the  class  to  which  this  or  that  isomeride  belongs. 
Moreover,  the  gathering  together  of  this  data  will  doubtless 
be  the  means  of  gaining  much  precise  knowledge  regarding 
the  relations  between  the  molecular  structure  and  the  actinic 
properties  of  compounds1.  For  the  experiments  of  Hartley2 
tend  to  the  conclusion  that  although  greater  or  less  absorp- 
tion is  connected  with  molecular  vibrations,  yet  the  special 
selective  absorption  characteristic  of  benzenoid  compounds  is 
rather  to  be  connected  with  atomic  vibrations.  These  ex- 
periments also  shew  that  the  mean  rate  of  vibration  of  the 
rays  absorbed  by  molecules  of  naphthalene  and  anthracene, 
is  less  than  that  of  the  rays  absorbed  by  benzene  molecules, 
and  hence,  remembering  the  similarity  of  the  character  of  the 
absorptions  in  these  three  cases,  it  is  concluded  that  the 
amplitudes  of  the  vibrations  of  the  naphthalene  and  anthra- 

1  For  the  application  of  his  general  conclusions  to  essential  oils,  quinoline, 
hydrocyanic  and  cyanuric  acids,  &c.,  see  Hartley,  C.  S.  Journal  Trans,  for  1880. 
676 ;  do.  for  1882.  45  ;  and  Chem.  News,  40.  269. 

2  C.  S.  Journal  Trans,  for  1881.  165—167. 


§  149]  APPLICATION   OF   PHYSICAL   METHODS.  333 

cene  molecules  are  greater,  and  the  rates  of  vibration  are 
slower,  than  those  of  the  benzene  molecules.  Hence  it  would 
follow  that  the  atomic  vibrations  which  probably  give  rise  to 
the  observed  selective  absorption  are  closely  dependent  on 
the  vibrations  of  the  molecules  as  wholes. 

Now  if  a  connection  between  the  vibrations  of  molecules 
and  the  vibrations  of  partsjof  these  molecules  is  established,  and 
if  this  connection  is  elucidated  by  precise  data,  we  shall  cer- 
tainly have  made  an  important  advance  in  solving  the  fun- 
damental problem  of  chemistry,  which  is  to  trace  the  relations 
between  the  composition  and  the  properties  of  bodies. 

A  further  step  in  this  direction  has  been  made  by  Abney 
and  Festing1,  who,  by  mapping  the  absorption  which  occurs 
in  the  infra-red  region  of  the  spectrum,  have  been  able  to 
shew  that  there  is  a  definite  connection  between  the  nature 
of  the  atomic  groups  in  the  molecules  of  many  carbon- 
compounds,  and  the  vibrations  of  the  rays  stopped  by  these 
compounds. 

149.  The  preceding  paragraphs  of  this  section  will,  I 
think,  shew  how  promising  of  important  results  is  the  applica- 
tion of  optical  methods  to  the  problems  of  chemical  statics. 
That  a  relationship  exists  between  refractive  power  and 
molecular  structure,  and  also  between  rotatory  power  and 
molecular  structure,  has  been  established.  In  the  hypo- 
thesis of  Briihl,  which  connects  the  former  physical  constant 
at  once  with  the  valencies  of  atoms  and  with  the  distribution 
of  atomic  interactions,  and  in  that  of  van't  Hoff,  which 
has  a  more  kinetical  aspect  than  the  hypotheses  regarding 
molecular  composition  at  present  dominant  in  chemistry, 
we  have  guides  to  future  research.  But  much  more  data, 
dealing  with  groups  of  allied  compounds,  must  be  brought 
together  before  either  of  these  hypotheses  can  be  fully  tested2. 

1  Proc.  R.  S.  31.  416,  and  Phil.  Trans,  for  1881/88;. 

2  Reference  may  here  be  made  to  a  paper  by  G.  Kriiss  [Her.  15.  1243,  and  16. 
2051]  on  an  optical  method  for  determining  whether  or  not  chemical  action  has 
occurred  between  two  substances  in  solution,   all  the  possible  products  of  the 
reaction  being  also  soluble  under  the  experimental  conditions.     The  method  con- 
sists, essentially,  in  comparing  the  sums  of  the  absorption-spectra  of  the  original 
liquids  with  the  absorption-spectrum  of  a  mixture  of  these  liquids. 


334  CHEMICAL  STATICS.  [§  150 


SECTION  III.    Methods  based  on  determinations  of  the  constant, 

formula-weight  1 

specific-gravity 

150.  The  quotient  obtained  by  dividing  the  formula- 
weight  by  the  specific  gravity  of  a  compound  (referred  to 
water  at  4°)  is  generally  called  the  specific  volume  of  that 
compound.  The  term  specific  volume,  however,  evidently 
expresses  the  relative  volume  of  unit  weight  of  the  substance. 
The  quotient  in  question  is  sometimes  called  the  molecular 
volume  of  the  compound  formulated.  This  expression  strictly 
interpreted  implies  that  the  formula-weight  is  identical  with 
the  molecular  weight,  and  that  the  specific  gravity  and 
formula-weight  are  expressed  in  terms  of  the  same  standard. 

The  value  of   —  — M —  is  equal  to  the  product  of  spe- 

spec.  gravity 

cific  volume  multiplied  into  molecular  weight,  assuming  the 
latter  to  be  the  same  as  the  formula-weight ;  or  we  may  say 
that,  if  the  weight  expressed  by  the  formula  is  taken  in  grams, 

,,  ,.     ,   formula-weight  ,,  ,         r      ,  . 

the  quotient  -  — g™  represents  the  number  of  cubic 

spec,  gravity 

centimetres  occupied  by  an  amount  of  the  substance  in  grams 
proportional  to  its  molecular  weight.  Now  we  can  determine 
the  molecular  weights  of  gaseous  compounds  only:  if  the 
specific  gravities  of  these  compounds  are  referred  to  hydrogen 

.          molecular  weight  ,  ,T 

as    unity,   then,  — ^  -   =  c,    and    c  =  2.      Never- 

spec.  gravity 

1  It  may  be  well  to  gather  together  here  references  to  the  most  important 
articles  and  papers  on  the  subject  of  this  section  : — KOPP,  Annalen  96.  153,  303  ; 
100.  19,  &c.  BUFF,  Annalen  Supplbd.  4.  129,  and  Ber.  4.  647.  THORPE, 
C.  S.  Jotirnal  Trans,  for  1880.  141,  327.  L.  MEYER,  Annalen  Supplbd.  5.  129; 
also  Die  modernen  Theorien  (4th  Ed.),  284 — 292.  ELSASSER,  Annalen  218.  302. 
WEGER,  Annalen  221.  61.  WATTS'S  Diet.;  1.  440  et  seq.  and  (more  especially)  3rd 
Supplt.  2117  et  seq.  RAMSAY,  C.  ^.y^rwa/Traiis.for  1879.  463  ;  do.  for  1881.  49. 
66.  LOSSEN,  Annalen  214.  81.  Compare  also  SCHIFF,  Ber.  14.  2761 ;  15.  1270; 
Annalen  220.  71,  278.  SCHALFEJEW,  Ber.  15.  2209;  16.  1853.  See  also 
O.  E.  Meyer's  Die  Kinetische  Theorie  der  Case,  216 — 221.  KRAFFT,  Ber.  15. 
1687.  WILSON,  Proc.  R.  S.  32.  457. 


§  I5'l]  APPLICATION    OF   PHYSICAL   METHODS.  335 

formula-weight    .       ,  ,   .      ,    r 

theless,   if  the   quotient   --  §7      is   obtained   for   a 

spec,  gravity 

number  of  liquid  compounds,  we  shall  have  a  series  of  com- 
parable values,  which,  —  if  formula-weight  of  liquid  is  a  simple 
multiple  of  molecular  weight  of  gas,  —  represent  the  volumes 
occupied  by  quantities  of  various  liquid  compounds  pro- 
portional to  the  molecular  weights  of  the  same  compounds  in 
the  state  of  gases. 

The  meaning  to  be  attached  to  the  expression  '  volume 
occupied  by  a  quantity  proportional  to  molecular  weight' 
will  be  discussed  in  paragraph  156. 

The  name  atomic  volume  is  generally  applied  to  the  quo- 

atomic  weight  ,  N 

tient  -  r-  --  f  ..     .  ,  —  i—       -  (water  =  i). 
spec,  gravity  of  liquid  element 

The  determinations  of  the  specific  gravities  of  liquids 
necessary  for  finding  values  for  the  quotient  we  are  discussing, 
should  be  made  under  comparable  conditions  as  regards 
pressure.  This  condition  is  fairly  fulfilled  by  determining  the 
specific  gravities  at  the  boiling  points  of  the  liquids1. 

formula-weight  of  liquid  compound 
151.     Let  the  quotient  -  —  ^  —  7— 

spec,  gravity  referred  to  water  at  4 

be  expressed  by  the  symbol  (  V}.  Then  the  value  of  (  V}  for 
a  compound  is  said  to  be  equal  to  the  sum  of  the  values  of 
(  V)  for  the  elementary  atoms  which  form  the  molecule  of 
that  compound.  But  has  each  elementary  atom  a  constant 
value  ? 

For  many  carbon  compounds  Kopp  has  shewn  that 


But  in  some  cases  the  observed  value  of  (  V)  does  not  agree 
with  that  calculated  by  this  formula  ;   thus 

diff. 

Aldehyde    C2H4O  :     calculated    (V)  =  (2  .  n)  +  (4  .  5'5)  +  7'8  =  sr8  : 

observed  (F)  =56*5.    +47 

Acetic  acid  C2H4O2  :  calculated  (  V]  =  (2  .  1  1  )  +  (4  .  5  -5)  +  (2  .  7-8)  =  59*6  : 

observed  (F)  =63-5.    +3-9 

1  Full  details  regarding  the  methods  for  accomplishing  this  will  be  found  in 
Thorpe's  paper,  loc.  tit.  ;  see  also  Ramsay  (loc.  tit.')  and  Schiff  (loc.  cit.}. 


336  CHEMICAL  STATICS.  [§151 

The  value  of  (  V)  for  a  compound  CxHyOz  is  conditioned, 
according  to  Kopp,  by  the  value  of  (  V)  for  the  oxygen  atom, 
or  atoms,  in  the  molecule.  Kopp  gives  the  following  two 
values,  according  as  the  oxygen  atom  acts  as  a  monovalent  or 
divalent  atom  in  the  given  molecule1. 

(F)OI==i2-2;    (F)On  =  7-8. 
Applying  these  values  to  the  case  of  aldehyde,  we  have 

(F)H3C—  C-0  =  (2.ii)  +  (4.5'5)  +  12-2  =  56-2; 
H 

a  result  which  agrees  very  closely  with  the  observed  value, 
viz.  56-5.     For  acetic  acid  we  have 

^O 

(  F)  H3C—  C<^       =  (2.  1  1)  +  (4.  5-5)  +  7-8  +  12-2  =  64-0  :  observed  =  63-5. 
OH 

Or  again,  for  ethylic  acetate, 

O 

(F)H3C  —  Cr  =(4.  ii)  +  (8.5'5)  +  i2-2  +  7-8=io8-o  : 

0-C2H5 

observed  ==107  '8. 

Or,  once  more,  for  acetone  and  its  isomeride  allylic  alcohol, 


(1)  (F)H3C  —  C  —  CH3  =  (3.ii)  +  (6.5'5)+i2'2  =  78'2:  observed  =  78*0  ; 

O 

(2)  (F)H2C-C-C-OH  =  (3.ii)  +  (6.5-5)  +  7-8  =  73-8:      „        =  73'8- 

H      H2 

Instead  of  assigning  two  values  to  the  oxygen  atoms  in 
compounds  of  the  form  C^H^O^  it  would  probably  be  better  to 
employ  the  value,  (F)  CO  =  23-2  (i.e.  11  +  12-2),  which  attri- 
butes the  influence  on  the  total  value  of  (F)  due  to  the 
presence  of  the  group  CO  to  both  the  atoms  which  com- 
prise this  group. 

Schiff  (loc.  cit.)  concludes  that  the  value  of  (  F)  O11  varies 
according  to  the  nature  and  arrangement  of  all  the  con- 

1  Kopp  used  the  expression  '  oxygen  within  the  radicle  '  as  synonymous  with 
what  is  now  called  divalent  (singly-linked)  oxygen  atoms  ;  and  '  oxygen  without 
the  radicle  '  as  synonymous  with  monovalent  (doubly-linked)  oxygen  atoms. 


§  152]  APPLICATION   OF   PHYSICAL  METHODS.  337 

stituents  of  the  molecule;  and  also,  that  the  value  of 
(V)X-C-Q  is  always  greater  than  that  of  ( V) C - O - X, 
when  X  represents  a  radicle. 

Kopp  deduced  two  values  for  (F)S;  thus  (F)SI=28'6, 
(F)SII  =  22'61:  but  only  one  value  for  (F)C,  and  one  for 
(F)H,  and  (F)C1.  Many,  and  very  varying  values,  have 
been  found  by  different  observers  for  ( F)N :  thus  Kopp 
assigns  the  value  2*3  to  ( F)N  when  N  occurs  in  amines,  and  17 
when  N  occurs  in  CN  and  in  some  nitro-compounds  ;  Ramsay 
gives  ( F)N  =  3*6  in  amines,  =  9*0  in  pyridine,  lutidine,  &c., 
and  =  7  in  aniline,  toluidine  and  dimethylaniline. 

152.  If  the  influence  exerted  by  the  oxygen  in  a  carbon 
compound  on  the  value  of  (V)  for  that  compound,  varies, 
according  to  the  actual  valencies  of  the  oxygen  atoms  in 
the  molecule,  it  appears  probable  that  the  total  value  of  ( F) 
will  also  depend  on  the  actual  valencies  of  the  carbon  atoms 
in  the  molecule.  Buff2  thought  that  his  determinations 
shewed  that  the  value  of  ( F)  for  compounds  containing  tri- 
valent  (doubly-linked)  carbon  atoms  is  greater  than  the  value 
calculated  on  the  assumption  that  (F)Cm=  (F)CIV=  I2'2. 
Thus, 

(1)  Dichlorethylene  C12  =  Cm  —  Cm  —  H2,  ( F)  =  79'9 : 

(F)  calculated  =  78 -6;  diff.  =  i'3  +  . 

(2)  Carbon  tetrachloride  C12  =  Cm  — Cm  =  Cl2,  (F)  =  ii5'4: 

(F)  calculated=ii3*2 ;  diff.  =  2'2  +  . 

H3CIV 

(3)  Amylene  >Cm—  C11  — CnIH2,  (F)  =  ii2  : 

H3CIV 

(F)  calculated  =i  10  ;  diff.  =  2'O+. 

(4)  Valerylene  H3CIV  —  Cm  —  C11  —  Cll\  —  CIVH3,  (F)  =  104-0: 

H  H 

(F)  calculated  =  99;  diff.  =  5'o+. 

(5)  Diallyl  H2Cm -  Cm - CIV - C1^ - Cm - CUIH2,  (F)=i26'8: 

ti         Jri2        H2       H 

(F)  calculated  =12 1 ;  diff.  =  5'8  +  . 

No  trustworthy  conclusions  regarding  the  values  to  be 
assigned  to  (F)Cm  or  (F)CIvcan  however  be  drawn  from 

1  See  also  Ramsay,  C.  S.  Journal  Trans,  for  1879.  471 — 2. 

2  Annalen,  Supplbd.  4.  143  et  seq. 

M.  C.  22 


33$  CHEMICAL  STATICS.  [§  153 

these  data,  because  when  we  tabulate  the  values  of  ( F)  for  a 
number  of  hydrocarbons  we  find  no  apparent  regular  con- 
nection between  these  values  and  the  valencies  of  the  carbon 
atoms.  Thus, 

(1)  Hexane  H3C  — (CH2)4  — CH3  (F)  =  i4o:  (F)  calculated  =143. 

(2)  Diallyl  H2C— C— C— C— C  —  CH2  (F)=i26'8:  „  „         =121. 

H     H2    H2    H 

CH 


(3)  Benzene     |  (F)=96:       „          „        =99. 

HC\/CH 

CH 

If  we  associate  the  increase  in  the  value  of  ( F)  for  diallyl 
over  the  calculated  value,  with  the  presence  of  trivalent 
carbon  atoms,  then  we  must  conclude,  that  in  the  molecule 
C6H6,  the  presence  of  trivalent  carbon  atoms  is  connected 
with  a  decrease  in  the  calculated  value  of  (F),  or  that  all 
the  carbon  atoms  in  this  molecule  are  tetravalent. 

153.  But  not  only  may  the  values  to  be  assigned  to  carbon 
and  oxygen  atoms,  in  determining  the  total  value  of  ( F)  for 
a  carbon  compound,  vary  according  to  the  actual  valencies  of 
these  atoms  in  the  molecule  of  the  compound  in  question,  but 
also,  apparently,  in  accordance  with  the  distribution  of  the 
interatomic  reactions  in  molecules  wherein  all  the  carbon 
atoms  are  tetravalent,  and  all  the  oxygen  atoms  divalent. 
Thorpe  (loc.  cit.)  has  given  some  examples  of  such  variations ; 
but  Zander1  has  extended  the  number  of  examples  con- 
siderably. Thus  a  comparison  of  ( F)  for  propyl  and  isopropyl 
compounds  shews  that  the  normal  compounds  always  exhibit 
a  smaller  value  than  the  iso-compounds : 

C3H7OH    C3H7I    C3H7Br    C3H7C1 

highest  value  of  ( F)  obtained  for  normal  \ 

,  /HoC  —  C  —  C  —  X\        (•        81-4      108-2    97-5       917 
compound^    •         H2    H2        )        ) 

lowest   value  of  (F)  obtained  for  iso- 


compound  ( X  — 

1  Annalen  214.  138:  224.  56. 


§I$3]  APPLICATION   OF  PHYSICAL  METHODS.  339 

but  the  molecules  of  both  classes  of  compounds  contain  only 
tetravalent  carbon  atoms1. 

Lessen2  has  collected  the  most  trustworthy  data  bearing 
on  the  question  as  to  whether  or  not  a  constant  value  can  be 
assigned  to  (F)CH2.  Kopp  gave  22  as  the  mean  value  for 
this  group.  Lessen  shews  that  the  differences  between  the 
values  of  (F)  for  successive  homologues  of  the  acid  series 
CwH2raflCO2H  nearly  agree  with  the  differences  calculated  on 
the  basis  of  (F)CH2  =  22  ;  but  that  in  the  series  of  alcohols 
CnH2n+1CH2OH  the  value  of  (F)CH2  varies  from  187  to  21, 
assuming  that  the  other  atoms  exert  a  constant  influence  on 
the  total  value  of  ( F).  Apparently  then  a  variable  value 
must  be  assigned  to  (F)CIV,  or  to  (F)H,  or  to  both  of  these 
quantities. 

Some  light  is  thrown  on  this  point  by  Zander's  comparison 
(loc.  cit.)  of  ( F)  for  propyl,  isopropyl,  and  allyl  compounds, 
which  leads  to  the  conclusion  that  the  difference  between  ( F) 
for  a  normal  propyl  and  the  corresponding  allyl  compound, 
i.e.  between  two  compounds  differing  in  composition  by  H2, 
varies  from  57  to  8*9  (having  a  mean  value  of  7*1)  :  hence,  if 
we  assume  that  the  difference  in  question  is  wholly  due  to  the 
difference  in  empirical  composition,  we  appear  forced  to  con- 
clude that  the  value  of  the  influence  exerted  on  (F)  by  the 
monovalent  atom  H  is  variable3. 

Thorpe  (loc.  cit.}  got  these  results  for  compounds  containing 
only  tetravalent  carbon  atoms  in  their  molecules  : 


1  See  also  Brown,  Proc.  R.  S.  26.  238.    Also  Elsasser,  Annalen  218.  302. 

2  Annalen  214.  81  et  seq. 

3  Besides  the  empirical  difference  of  H2,  there  is  a  difference  in  the  actual 
valencies   of  some    of   the    carbon   atoms    in    propyl    and    allyl   compounds ; 
thus,   normal    propylic  alcohol    =    H3C  —  C  —  C  —  OH,    and    allylic   alcohol 

H2    H2 

=  H2Cm  —  Cm  —  C  —  OH.    See  also  Weger,  Annalen  221.  61,  who  gets  different 
H         H2 

values  for  ( V)  CH2  in  different  series  of  compounds.  See  Ber.  16.  2458,  where 
Kopp  reminds  us  that  this  number  was  given  by  him  as  a  mean  value,  and 
nothing  more.  Schiff  (Annalen  220.  286,  and  291)  concludes  that  (F)C  almost 
certainly  varies  according  to  the  nature  and  the  arrangement  of  the  constituents  of 
the  molecule  in  which  C  occurs. 

22 — 2 


340  CHEMICAL  STATICS.  [§  J53 

H2CC12(F)=  65-12;  hence  (J7)Cl  =  2i-6;  (assuming  (F)C=n, 


F)=  84-53;      „ 
CC14(F)=  103-68;      „      (F)Cl=23-2 

Taking  the  mean  value  for  (  F)C1,  viz.  227,  and  applying  this 
to  calculate  the  values  of  (V)  for  each  of  the  preceding  com- 
pounds, we  have 

(F)H2CC12=  67-4        observed=  65-12        diff.  =  2'28- 
(F)HCC13=  84-53  „        =  84-53          ,,   =o'o 

(F)     CCl4=ioi-8  „        =103-68          „   =1-88  + 

Hence  the  value  of  (  F)C1  appears  to  be  variable.  This  is  more 
strikingly  illustrated  by  Staedel's  comparison1  of  the  differences 
in  the  values  of  (  V),  and  also  the  differences  in  the  boiling 
points,  at  various  pressures,  of  chlorine  compounds  derived 
from  C2H4. 

The  differences  in   (F),  and   also  in   B.P.  between  the 
following  pairs  of  compounds,  viz. 

C1H2C  —  CH2C1  and  H3C  —  CH2C1, 
C1H2C  —  CHC12  and  H3C  —  CHC12, 
C1H2C  —  CC13  and  H3C  —  CC13, 

express  differences  corresponding  with  change  of  CH3  into 
CH2C1,  i.e.  with  the  introduction  of  the  first  chlorine  atom  in 
place  of  an  atom  of  hydrogen  into  the  hydrocarbon  residue 
CH9. 

The  differences  in  the  values  of  the  same  quantities  be- 
tween the  following  pairs  of  compounds,  viz. 

C12HC  —  CH3  and  H2C1C  —  CH3, 
C12HC—  CH2C1  and  H2C1C  —  CH2C1, 
C12HC  —  CHC12  and  H2C1C  —  CHC12, 
C12HC  —  CC13  and  H2C1C—  CC13, 

express  differences  corresponding  with  the  introduction  of  the 
second  chlorine  atom  (in  place  of  an  atom  of  hydrogen)  into 
the  residue  CH3. 

1  Ber.  15.  2559. 


§  154]  APPLICATION   OF  PHYSICAL  METHODS.  341 

And  lastly,  by  comparing  ( V)  and  B.P.  for  the  following 
pairs  of  compounds,  viz. : 

C13C  — CH3  and  C12HC  — CH3, 
ClgC  —  CH2C1  and  C12HC— CH2C1, 
C13C  —  CHC12  and  C12HC  — CHC12, 
C13C  — CC13  and  C12HC  — CC13, 

the  differences  corresponding  with   the   introduction   of  the 
third  chlorine  atom  into  the  group  CH3  are  determined. 
Now  the  differences  in  question  are : 

for  the  first  chlorine  atom  ( V}  =  14*20  :  B.P.  =  56°'22  ; 
„       second        „  ( V}  =  16-37  :  B.P.  =  3i°'3o ; 

„       third  „  (F)=i9'i6  :  B.P.  =  i6°'04. 

Hence  each  chlorine  atom  has  a  different  'volume-value* 
and  a  different  'boiling-point-value.'  If  we  choose  to  at- 
tribute the  observed  differences  to  the  carbonaceous  parts  of 
the  molecules,  i.e.  to  C2H4  in  C2H4Cl2,to  C2H3  in  C2H3C18,  &c., 
we  seem  still  obliged  to  admit  that  carbon  and  hydrogen 
atoms  have  varying  'volume-values',  and  varying  'boiling- 
point-values  ',  in  the  molecules  formulated. 

1 54.  The  remark  made  in  paragraph  151  that  the  value 
of  (V)  for  a  compound  is  equal  to  the  sum  of  the  values  of 
( V)  for  each  of  the  elementary  atoms  in  the  molecule  of  that 
compound,  must  evidently  be  supplemented  by  the  statement, 
that  in  the  case  of  carbon  compounds,  at  any  rate,  the  value  of 
( V)  is  not  constant  for  C  or  O,  and  probably  not  for  H  or 
Cl,  but  varies  in  accordance  with  (i)  the  actual  valencies  of 
the  former  pair  of  atoms,  and  (2)  the  distribution  of  all  the 
atomic  interactions  in  the  molecule.  The  precise  character 
of  the  connection  between  the  values  of  ( V)  for  C,  O,  H,  and 
Cl,  and  the  valencies  on  the  one  hand,  and  the  nature 
of  the  atoms  (or  atomic  groups)  in  direct  union  within  any 
molecule  on  the  other  hand,  cannot  be  ascertained  until 
much  more  experimental  data  has  been  accumulated1.  The 
known  data  regarding  the  values  of  ( V)  cannot  therefore  be 

1  It  is  pointed  out  by  Lessen  (loc.  cit.}  that  careful  determination  of  ( V)  for 
many  series  of  carbon  compounds  and  for  many  individuals  in  each  series,  are 
now  required. 


342  CHEMICAL  STATICS.  [§  *55 

applied  in  other  than  a  very  tentative  way  to  the  selection  of 
one  from  among  several  possible  structural  formulae1. 

155.  The  values  of  (V)  for  many  solid  compounds  have 
been  compared,  and  attempts  have  been  made  to  generalise  the 
relations  between  these  values  ;  but,  as  might  be  expected  from 
considering  how  little  comparable  are  the  conditions  under 
which  the  densities  of  solids  have  been  determined,  the  con- 
clusions are  either  vague  and  difficult  of  precise  application, 
or  represent  only  interesting  relations  between  certain  numbers, 
without  much,  if  any,  connection  with  chemical  facts. 

By  considering  the  difference  between  (  F)MO  and  (  F)M, 
a  fairly  constant  value  for  (F)O  in  the  oxides  is  sometimes 
obtained  :  thus  for  PbO  and  Fe2O3,  the  difference  in  question 
is  about  5*5.  But  in  other  oxides  the  value  of  (F)O  appears 
to  be  very  variable  ;  thus, 

(F)Cu  =  5'i;  but  (V)  Cu2O  -(V)  Cu2=io'5. 


Brauner  and  Watts2  have  drawn  the  following  conclusions 
from  comparisons  of  (F)MO  and  (F)M  for  different  series 
of  oxides. 

(1)  In  strongly  basic  oxides  the  value  of  (  F)O  is  negative  ; 
the  more  basic  the  oxide,  and  the  greater  the  value  of  (F)M 
in  the  oxide,  the  more  negative  is  the  value  of  (F)O. 

(2)  In  oxides  of  heavy  metals  and  non-metals  the  value  of 
(F)O  is  positive. 

(3)  In  oxides  of  the  earth  metals  the  value  of  (  F)O  is  nil. 
The  values  of  (  F)  for  isomorphous  compounds  generally 

vary  little;  thus, 

(F)MgO.Al2O3=4i-4  (F)  ZnO.Fe2O3=47'o 

(F)  ZnO  .  A12O3=40'2  (V]  MnO  .  Cr2O3=46'4. 

The  greater  the  agreement  between  the  angles  of  crystals 

1  An  illustration  of  the  difficulties  which  are  met  with,  and  of  the  uncertain 
nature  of  the  results  obtained,  is  furnished  by  the  contradictory  conclusions  of 
Thorpe  (see  Watts's  Diet.  3rd  Supplt.  2117  —  18)  and  of  Masson  and  Ramsay  (see 
C.  S.  Journal  Trans,  for  1881,  51  etseq.)  regarding  the  structural  formula  of  POC13. 
Thorpe  concludes  that  the  formula  ought  to  be  written  C12  =  P  —  O  —  Cl,  Masson 
and  Ramsay  think  that  C13=E  P  —  O  more  nearly  represents  the  facts. 

2  Phil.  Mag.  [5]  11.  60. 


§  155]  APPLICATION   OF   PHYSICAL   METHODS.  343 

belonging  to  the  same  class,  the  less  does  the  value  of  (V) 
differ,  e.g. 


45'8   crystals  exhibit  differences  from  those  of  SrCO3  and 

PbCOg1. 

Kopp2  has  concluded  that  if  D,  the  difference  between 
what  he  calls  the  '  molecular  volumes  '  of  two  isomorphous 

compounds,  is  represented  as  D=  ^    ^      (  J7\~\  '  t^ien  t^le  va*ue 

of  D  may  attain  a  maximum,  equal  to  0*328,  without  isomor- 
phism being  impossible. 

Determinations  of  (  V)  for  anhydrous  and  hydrated  salts 
promise  to  throw  some  light  on  various  questions  implied  in 
the  commonly  used  expressions  'water  of  crystallisation  '  and 
'water  of  constitution.' 

Graham  distinguished  (  saline  '  water  from  '  basic  '  water  in 
salts  and  acids  ;  the  replacement  of  the  former  by  another  salt, 
or  by  an  oxide,  produced  a  double  —  or  in  the  case  of  acids  a 
normal  —  salt  ;  the  replacement  of  the  'basic'  water  in  an  acid 
produced  a  basic  salt.  Thus, 

MgSO4H2O6H2O  gave  MgSO4K2SO46H2O  ; 

saline   basic 

N2O5H2O3H2O  gave  fN2O5CuO3H2O  normal  nitrate  of  copper. 

saline  basic  JN2O5CllO3CuO  baSlC  „ 

Graham  further  distinguished  basic  water  from  water  of 
constitution;  e.g. 

H2SO4.H2O,   from     C2O3.H2O. 

basic  constitutional 

Thorpe  and  Watts3  have  determined  (V)  for  the  salts 
MSO4,  when  M  =  Mg,  Zn,  Cu,  Mn,  Fe,  Co;  and  for  the  hy- 
drated salts  MSO4^H2O  when  M  =  Mg,  Zn,  &c.  and  x  varies 
from  i  to  7. 

1  For  more  details  see  Naumann's  Handbuch  der  Allgemeinen  und  Physikal- 
ischen  Chemie,  360  —  362. 

2  Annalen  36.  i.     Pogg.  Ann.  52.  262;  53.  446;  56.  371.     See  also  article 
"  Isomorphie,"  in  the  Nenes  Handworterbuch  der  Chemie. 

3  C.  S.  Journal  Trans,  for  1880,  102. 


344  CHEMICAL  STATICS.  [§  155 

The  value  of  (  F)MSO4  was  found  to  be  independent  of  the 
nature  of  M  for  the  dehydrated  salts.  The  difference 
(  F)MSO^H2O-(  F)MSO4  gave  the  increase  in  (  F)  for  *H2O 
added  to  the  salts.  The  following  results  were  obtained. 

Mean  difference  in  value  of 

(V)S  and  (F)S.H20  =107 

(F)S.H20          „ 

(F)S.2H20        „ 

(F)S.3H20        „ 

(F)S.6H2O 


Hence  the  value  of  (F)MSO^H2O  is  influenced  in  a 
different  degree  by  each  of  the  molecules  of  water  which  com- 
bines with  the  salt;  or,  it  may  be  said,  that  the  water  molecules 
contribute  in  unequal  degrees  towards  the  total  value  of  (  F). 

Clarke1  has  compared  the  differences  between  (F)  for 
hydrated  and  (F)  for  dehydrated  salts,  belonging  to  two 
classes  of  compounds. 

In  the  first  class,  where  M  =  Ca,  Sr,  Ba,  Mg,  Cu,  Fe,  or  Co. 
and  x  varies  from  2  to  6,  the  mean  value  of 

(  V]  MCl2:rH2O  -  (  F)  MC12 

x 

was  found  to  be  =  13  76  (with  a  maximum  value  of  15*0,  and  a 
minimum  of  I2'5). 

The  second  class  comprised  various  hydrated  oxides  and 
hydroxides,  viz. 

B2033H20,  I206H20,  K2OH20,  CuOH2O,  SrOH2O,  BaOH2O, 
A1203H2O,  Mn2O3H2O,  Fe2O3H2O. 

In  this  class  the  value  of  the  difference 

(  V]  oxide  *H20-(F)  oxide 
x 

varied  from  7*4  to  19*4. 

If  S  represent  one  of  the  chlorides  .  belonging  to  the  first 
class,  or  one  of  the  oxides  belonging  to  the  second  class,  then, 
for  class  I,  the  formula  (  F)S  ^H2O  =  (  F)S  +  (x  .  1376)  gives 

1  Amer.  Journal  of  Sci.  and  Arts,  (3).  8.  428. 


§  156]  APPLICATION  OF  PHYSICAL  METHODS.  345 

results  which  agree  fairly  well  with  the  observed  results ;  but 
no  such  simple  relation  between  ( F)S  #H2O  and  ( F)S  can  be 
traced  among  the  results  obtained  for  compounds  belonging 
to  class  II. 

But  the  hydrates  of  class  I  belong  to  the  group  of  com- 
pounds containing  'water  of  crystallisation/  whereas  those 
of  class  II,  or  most  of  them  at  any  rate,  belong  to  the  group 
containing  '  water  of  constitution ' ;  hence,  although  the  results 
obtained  by  Thorpe  and  Watts  (loc.  cit!)  lead  to  the  conclusion 
that  the  value  of  ( F)H2O  in  the  salts  MC1^H2O  is  probably 
different  for  each  addition  of  H2O,  nevertheless  Clarke's  num- 
bers, taken  as  a  whole,  emphasise  the  difference  between 
'  water  of  crystallisation '  and  'water  of  constitution/ and  shew 
that  the  chemical  difference  implied  in  these  expressions  is 
connected  with  the  relative  magnitudes  of  the  spaces  occupied 
by  chemically  comparable  quantities  of  hydrated  salts  belong- 
ing to  each  group  of  compounds. 

i     — ,  .     .  formula-weight ,      .  , 

156.     The  quotient rE—     -^—  has  been  treated  as  an 

specific  gravity 

empirically  determined  quantity :  incidentally  it  has  been 
regarded  as  expressing  the  volume  occupied  by  a  quantity  of 
the  compound  formulated  proportional  to  the  weight  of  the 
molecules  which  form  the  vapour  of  that  compound.  The 
question  is  often  propounded  in  papers  on  ' Specific  volumes', 
whether  the  volume  of  an  element  in  the  free  state  is,  or  is 
not,  identical  with  the  volume  of  the  same  element  in  combi- 
nation. This  question,  it  seems  to  me,  may  be  better  put  in 
another  form.  What  is  the  connection  between  the  value  of 
(  V)  for  a  given  compound,  and  the  nature  and  arrangement 
of  the  atoms  which  constitute  the  molecule  of  that  compound? 
It  has  been  shewn  (pars.  152,  153)  that  the  partial  value  to 
be  assigned  to  each  atom  is  not  a  constant  quantity ;  in  other 
words  that  (F)  varies  with  variations  in  the  arrangement, 
no  less  than  in  the  nature  of  the  atoms  which  form  the 
molecule  of  the  compound  for  which  (  F)  has  been  determined. 
But  is  there  any  connection  between  the  variations  of  (F), 
the  valencies  of  the  atoms  on  the  one  hand,  and  the  distribu- 
tion of  the  interatomic  reactions  on  the  other  ?  From  the 


346  CHEMICAL  STATICS.  [§  156 

data  concerning  isomeric  carbon  compounds,  firstly,  containing 
only  saturated  polyvalent  atoms,  and  secondly,  containing 
also  unsaturated  polyvalent  atoms,  we  may  conclude,  I  think, 
that  both  connections  exist.  It  seems  probable  that  a  decrease 
in  the  actual  valency  of  an  atom,  other  things  remaining  the 
same,  is  attended  by  an  increase  in  the  value  of  ( V).  But 
Staedel's  investigation  (par.  153)  shews  that  the  latter  value  is 
also  modified  by  the  nature  of  all  the  atoms  in  the  molecule. 
If  these  connections  can  be  made  precise,  and  their  nature  as- 
certained by  careful  investigation,  it  may  become  possible  to 
trace  relations  between  the  volumes  occupied  by  molecules  of 
defined  structure  and  the  energy-differences  of  these  mole- 
cules, and  perhaps  to  connect  with  these,  the  differences  in 
the  values  of  the  refractive,  and  the  rotatory  powers,  of  the 
same  molecules1. 

If  the  value  of  ( V)  for  a  compound  is  regarded  from  the 
point  of  view  of  the  molecular  theory,  a  connection  may  be 
traced  between  this  value,  and  the  partial  value  of  (  F)  for  each 
atom  in  the  molecule  of  the  compound.  For  it  has  been  shewn 
by  L.  Meyer2,  and  by  Loschmidt3,  that  the  spaces  occupied 
by  gaseous  molecules  (calculated  from  data  based  on  the 
transpiration-coefficients  of  the  substances)  are  connected  with 
the  atomic  structure  of  these  molecules,  in  the  same  general 
way  as  has  been  shewn  by  Kopp  and  others  to  hold  in  the 
case  of  liquid  compounds4.  The  Clausian  sphere-of-action 
(wirkungssphdre}  of  a  molecule  is  the  smallest  space  which  the 
molecule  can  occupy  under  given  conditions.  Changes  in 
these  conditions  (e.g.  change  of  temperature),  changes  in  the 
form  of  the  molecule,  or  changes  in  the  arrangement  of  the 
atoms  in  the  molecule,  will  be  accompanied  by  changes  in  the 

1  We  should  thus  gain  clearer  conceptions  of  the  properties  of  atoms  as  these 
are  exhibited  in  atomic  interactions,  and  also  be  able  to  connect,  in  a  more  precise 
manner  than  is  yet  possible,  these  interactions  with  the  properties  of  the  systems 
thereby  formed.     If  this  view  is  accepted  it  is  evident  that  the  results  obtained  by 
the  various  physical  methods  discussed  in  this,  and  the  preceding  section,  must  have 
kinetical  as  well  as  statical  aspects  (see  book  n.  chaps,  in.  and  IV.). 

2  Annalen,  Supplbd.  5.  129. 

3  Sitzberichte  der  K.  Akad.  zu  Wien  (niath.-naturwiss.  classe).  52.  (2nd  part)  395. 

4  See  O.  E.  Meyer's  Die  Kinetische  Theorie  der  Case,  216 — 221. 


§  156]  APPLICATION   OF   PHYSICAL  METHODS.  347 

space  occupied  by  the  molecule.  The  relations  between  the 
values  of  these  smallest  spaces  (spheres-of-action)  occupied  by 
the  molecules  of  two  gases  can  be  calculated,  by  means  of  a 
formula  deduced  from  the  general  principles  of  the  molecular 
theory,  from  observations  of  the  transpiration-coefficients  of 
the  gases.  Putting  the  experimentally  determined  value  of 
(  V)  as  the  value  of  the  molecular  sphere-of-action  of  one  of 
the  gases,  the  values  of  the  molecular  spheres-of-action  of  other 
gases  can  be  found,  and  compared  with  those  calculated  from 

,  ,  T  i        r      atomic  weight 

Kopps,  Meyers,  and  Loschmidts  values  for r^ —-- 

specific  gravity 

of  nitrogen,  oxygen,  hydrogen1,  &c.,  and  from  the  partial  values 
assigned,  by  different  chemists,  to  various  atoms  in  determining 
the  total  value  of  (  V)  for  molecules  containing  these  atoms. 
This  is  done  by  O.  E.  Meyer  (loc.  cit.  pp.  219 — 221).  The 
observed  and  calculated  values  of  (V)  agree  as  closely  as 
could  be  expected,  considering  that  regard  has  been  paid  in  the 
calculations  solely  to  volume,  whereas  the  molecular  spheres- 
of-action  must  be  conditioned  by  the  form,  the  diameter,  and 
the  length  of  the  molecular  systems2.  Hence  there  is  a  well- 
established  probability  in  favour  of  the  conclusion  that  the 
partial  values  assigned  to  each  atom,  in  determining  the  total 
value  of  ( V)  for  a  liquid  compound,  are  proportional  to  the 
volumes  occupied  by  these  atoms  in  the  gaseous  state.  But 
this  is  just  the  conclusion  drawn  from  an  empirical  study  of 
the  values  of  (  V)  determined  for  series  of  liquid  compounds. 
Much  work  must  however  be  done  before  precise  connections 


1  For  a  description  of  the  determination  of  this  constant  for  oxygen  and  other 
gases  from  measurements  of  the  transpiration-coefficients  of  these  gases,    see 
L.  Meyer,  Annalen,  Supplbd.  5.  129. 

2  Meyer  (loc.  cit.  pp.  213 — 216)  concludes  that  probably  the  atoms  in  the 
molecules  H2,  C12,  O2,  N2,  HC1,  NO,  H2O,  and  H2S  are  arranged  rectilinearly 
in  an  open  chain;  the  atoms  in  the  molecules  CO2,  N2O,  C2N2,  and  NH3  are 
arranged  in  one  plane  but  not  rectilinearly ;  the  atoms  in  the  molecule  CH4  form 
a  sphere;  and  those  in  the  molecules  CH3C1,  C2H4,  C2H5C1,  and  C2H6O  form 
oblate  spheroids.      Boltzmann   [Wied.  Ann.   18.   309  (also  Her.  16.    772)]    has 
drawn  conclusions  as  to  the  forms  of  various    molecules,  from   determinations 
(chiefly  those  made  by  Strecker)  of  the  ratio  of  specific  heat  at  constant  pressure 
to  that  at  constant  volume. 


348  CHEMICAL  STATICS.  [§  r57 

can  be  traced  between  the  total  value  of  ( F)  and  the  partial 
values  assigned  to  the  various  atoms  in  any  molecule. 


SECTION  IV.     Method  based  on  the  determination  of 
'  Etherification-v  alms1! 

157.  The  rate  of  formation  of  ethereal  salts  by  the  mutual 
actions  of  alcohols  and  carbon-containing  acids  has  been 
studied  by  Menschutkin  :  many  of  his  results  have  a  direct 
bearing  on  the  questions  of  chemical  kinetics,  some  of  them 
however  may  find  a  place  here.  The  standard  reactions  in 
terms  of  which  determinations  are  stated  are  these, 

(1)  HCH2OH  +  CH3CO2H  =  CH3CO2(CH3)  +  HOH  ; 

XCH3 

(2)  HC  —  CH2OH  +  H  .  C02H  =  HCO2(C4H90)  +  HOH. 


By  varying  the  alcohol  in  (i)  and  the  acid  in  (2),  comparable 
series  of  values  are  obtained  for  (i)  alcohol-acetic  system,  and 
(2)  acid-isobutylic  system.  The  number  of  molecules  of 
HCH2OH  decomposed  in  reaction  (i),  and  the  number  of 
molecules  of  HCO2H  decomposed  in  reaction  (2),  when 
equilibrium  is  established,  are  taken  as  100,  and  the  results  with 
other  alcohols  and  acetic  acid,  or  with  other  acids  and  iso- 
butylic  alcohol,  are  stated  in  terms  of  this  unit. 

The  expression  '  etherification-velocity  '  is  used  to  denote 
the  amount  of  action  during  one  hour  ;  the  expression  'etheri- 
fication-limit  '  is  used  to  denote  the  amount  of  action  when 
equilibrium  is  established.  Thus  the  statement  'the  etherifica- 
tion-velocity of  CH3CH2OH  is  67  '3,  and  the  etherification- 
limit  is  95*6'  means,  that  when  equal  numbers  of  molecules 
of  CH8CH2OH  and  CH3CO2H  react,  67-3  molecules  of 
CH8CH2OH  are  decomposed  during  the  first  hour,  and  95*6 

1  The  papers  by  Menschutkin,  of  which  this  section  is  a  very  condensed 
summary,  will  be  found  in  J.  fiir  prakt.  Chemie,  (2)  24.  49:  do.  25.  193,  and  203 
(abstracts  in  C.  S.  Journal  for  1881.  1117;  1882.  384,  485,  and  595).  Abstracts 
will  also  be  found  in  Ber.  14.  2630,  2819:  15.  162,  248,  and  721.  A  paper  con- 
taining a  summary  of  Menschutkin's  results  will  be  found  in  Ann.  Chim.  Phys. 
(5).  30.  81.  (Abstract  in  C.  S.  Journal  for  1884.  726.) 


§158]  APPLICATION   OF   PHYSICAL  METHODS.  349 

when  the  action  ceases,  the  number  of  molecules  of  HCH2OH 
decomposed  under  similar  conditions  (at  the  close  of  the 
reaction)  being  taken  as  loo1. 

158.  The  following,  among  many  other  numbers,  were 
obtained  by  Menschutkin. 

Alcohol-acetic  system. 

Formula  of  alcohol.  Velocity.  Limit. 

HCH2OH  80-0  loo-o 

CH3.CH2OH  67-3  95*6 

C2H5.CH2OH  66-9  96'o 

Hence,  the  substitution  of  CH3  for  H  in  the  primary  alcohol 
H .  CH2OH  appears  to  be  accompanied  by  a  decrease  in  the 
etherification-velocity  of  about  12*5,  and  in  the  limit  of  about  4*5. 
The  following  conclusions  are  drawn  by  Menschutkin  from 
his  determinations  of  the  reaction-values  of  the  system 
R.CH2OH  +  CH3C02H. 

(1)  The   reaction-values  (i.e.  velocity  and    limit)  of  the 
normal   group   CnH2n+1   in   the   alcohols  CnH2n+1CH2OH  are 
practically  the  same. 

(2)  Isomerism  in  the  CwH2n+1  radicles  of  primary  alcohols 
influences  only  the  velocity-value,  not  the  limiting  value. 

(3)  Unsaturated  alcohols  (R.CH2OH)  exhibit  lower  re- 
action-values  than  saturated   alcohols;   e.g.   the   values   for 
C2H3-CH2OH  are  smaller  than  those  for  C2H6-CH2OH. 

From  his  study  of  the  etherification  of  secondary  alcohols, 
R2CHOH,  the  same  chemist  concludes  that  these  alcohols 
exhibit  lower  values  than  primary  alcohols ;  and  that  the 
same  radicle  has  smaller  values  in  a  secondary  than  in  a 
primary  alcohol.  The  limiting  value  for  tertiary  alcohols 
cannot  be  determined  on  account  of  the  occurrence  of 
secondary  changes  ;  the  velocities  shew  great  irregularities. 

Further  results  obtained  by  Menschutkin  shew  that  definite 
connections,  the  nature  of  which  cannot  yet  be  precisely 

1  The  process  is  conducted  at  153° — 154° ;  the  residual  acid  is  determined  by 
titration.  Two  to  five  grams  of  alcohol  are  sufficient,  and  the  process  is  always 
applicable  except  the  ethereal  salt  produced  happen  to  be  unstable  at  the  tempera- 
ture of  experiment. 


35O  CHEMICAL  STATICS.  [§  158 

traced,  exist  between  the  actual  valencies  of  the  atoms,  and 
also  the  distributions  of  the  interatomic  reactions  in  the 
molecules  of  alcohols,  and  the  etherification-values  of  these 
alcohols1. 

By  multiplying  the  limiting  value  of  each  compound  by 
the  molecular  weight  of  that  compound  (and  dividing  by  100), 
numbers  are  obtained  which  exhibit  the  influence,  on  the 
etherification-limit,  of  the  molecular  weights  of  the  members  of 
the  system  studied.  Menschutkin  gives  the  following  numbers 
as  representing  molecular  limits.  In  a  later  paper  he  calls 
these  numbers  simply  weight-limits,  in  distinction  to  the  per- 
centage limits  already  explained. 

Acid-isobutylic  system. 

Molecular     Difference  for 
Acid.  limit.  each  CH,. 


CH3C02H 

4o*42\ 

C2H5CO2H 

50*83  / 

10*41 

(C3H7«)C02H 
(C6Hua)C02H 

6i*i7< 
80*98  X 

I0'34     i9-8z 

c\*c\r\ 

99°        2 

(C7H15«)C02H 

102*05^ 

21*07 

in'C?  —  L 

Mean  difference  for  each  increment  of  CH2=  10*29. 

The  value  of  the  molecular,  or  weight,  limit  for  any  mem- 
ber of  this  series  of  acids  (the  alcohol  being  isobutylic)  may 
be  found  by  the  formula, 

molecular  limit  =40*42  +  (n  -  2)  10*29  5 

when   n  =  number  of  carbon  atoms  in  the  molecule  of  the 

acid. 

Thus,  in  the  acid  (C8H7a)  CO2H  n  =  4,  hence 

molecular  limit  =  40 "42 +  (2.  io'29)  =  6ro;  observed  value  =  6r  17. 

Menschutkin  gives  the  expression  a  +  (n-  2)  d  for  finding 
the  molecular  etherification-limit  for  an  acid  in  any  system  of 
alcohol  and  acids,  when  a  =  molecular  limit  for  the  first  acid 
of  the  series,  and  d—  mean  increase,  for  each  increment  of 
CH2,  in  the  molecular  limit  of  the  acids  of  the  series. 

1  For  a  more  precise  statement  of  Menschutkin's  conclusions  on  this  point  see 
abstract  in  Ber.  14.  2818. 


§  158]  APPLICATION   OF   PHYSICAL   METHODS.  351 

The  rule  is,  to  the  value  of  the  limit  for  the  given  alcohol 
with  the  first  acid  of  the  series,  add  (n  —  2)  d,  that  is,  add  (n  —  2) 
times  the  mean  homologous  difference  (i.e.  the  mean  differ- 
ence for  each  increment  of  CH2)  between  the  weight-limits  of 
the  given  acid  and  the  first  acid  of  the  series,  when  n  =  number 
of  carbon  atoms  in  the  molecule  of  the  given  acid. 

Thus,  required  the  weight-limit  for  the  caproic-butylic 
system.  For  the  acetic-butylic  system  a  =  40*52,  and  d=  10*29; 
caproic  acid  is  C5Hn  .  CO2H  ;  therefore  the  weight-limit  re- 
quired is  40*52  +  (4 .  10*29)  =  81*68. 

It  is  evident  that  the  percentage  limit  can  easily  be  found 
when  the  values  of  a  and  d  are  given.  In  the  case  in  question 
we  have, 

percentage  limit = ^—  =  70*41.     [C6HU .  CO2H  =  1 16]. 

Menschutkin  gives  the  following  values  for  a,  and  dy  in 
various  systems  of  alcohols,  and  acids  of  the  acetic  series  : 


=  10-29. 


It  is  also  possible  to  vary  the  alcohol,  the  acid  remaining 
constant,  and  from  data  obtained  to  calculate  the  weight-limit 
for  any  given  system1. 

From  a  comparison  of  the  etherification-values  for  primary, 
secondary  and  tertiary  acids,  and  also  of  the  same  values  for 
hydroxy-  and  chloro-acids,  &c.,  Menschutkin  draws  certain 
conclusions  regarding  the  connections  between  the  variations 
in  these  values  and  the  molecular  structures  of  the  various 
acids.  For  instance,  the  velocity  of  etherification  of  the 
primary  acids  is  much  greater  than  that  of  the  secondary 
acids,  but  the  limiting  values  are  nearly  identical  in  both 
series. 

1  See  details  in  C.  S.  Journal,  Abstracts  for  1882,  387. 


acid-ethylic     system 

#  =  39'94   " 

acid-propylic        „ 

#  =  40-23 

acid-butylic          „ 

#=40*42 

acid-amylic          ,, 

#  =  40-55 

acid-hexylic         „ 

#  =  40*64 

acid-heptylic        „ 

#  =  4071 

acid-caproic         „ 

#=4077    - 

352  CHEMICAL  STATICS.  [§  159 

A  study  of  these  conclusions  shews  that  much  is  to  be 
hoped  for  from  the  application  of  Menschutkin's  method,  but 
that  more  data  must  be  obtained  before  we  have  precise 
knowledge  concerning  the  connections  in  question1. 

Concluding  Remarks  on  Part  I. 

1 59.  The  general  aim  of  the  first  part  of  this  book  has  been 
to  give  a  fairly  complete  account  of  the  present  state  of  know- 
ledge regarding  the  questions  of  chemical  statics,  indicating 
where  such  knowledge  requires  to  be  chiefly  supplemented, 
or  rendered  more  precise,  by  new  experimental  researches. 

I  have  regarded  those  questions  which  are  concerned  with 
substances,  or  systems  of  substances,  in  equilibrium  as  broadly 
belonging  to  chemical  statics  ;  but  I  have  been  obliged  to 
pay  more  or  less  attention  to  the  kinetical  aspects  presented 
by  all  such  questions. 

It  may  be  said  that  the  fundamental  conception  of  atom 
and  molecule,  stated  and  illustrated  in  chapter  i.,  has  been 
regarded  in  its  applications  to  explain  resemblances  and 
differences  between  physical  and  chemical  phenomena,  nascent 
actions,  allotropy,  isomerism,  and  the  classification  of  elements 
and  compounds  ;  and  that  the  principal  methods,  both  purely 
chemical  and  chemico-physical,  which  are  employed  in  ex- 
amining these  problems,  have  been  sketched,  and  their  appli- 
cations illustrated. 

A  way  has  thus  been  cleared  by  which  we  may  hope  to 
approach  the  more  difficult  problems  of  chemical  kinetics. 

1  See  some  of  Menschutkin's  generalisations  in  C.  S.  Journal,  Abstracts  for 
1882,  485,  598 :  and  an  application  to  the  formulae  of  maleic  and  fumaric  acids 
in  do.  do.  1882,  383. 

Schiff  (Annalen  223.  47 ;  abstract  in  C.  S.  Journal  for  1884,  808)  has  deter- 
mined the  '  coefficients  of  capillarity '  of  a  number  of  liquid  carbon  compounds. 
There  appears  to  be  a  distinct  connection  between  the  values  of  this  constant  and 
the  nature,  number,  and  arrangement  of  the  atoms  in  the  molecules  of  the  com- 
pounds examined. 

Perkin  has  just  published  an  extensive  research  into  the  connections  between 
the  composition  of  various  carbon  compounds  and  their  power  of  rotating  the 
plane  of  polarisation  of  a  ray  of  light  when  under  magnetic  influence.  (C.  S. 
Journal^  Trans,  for  1884,  421  et  seq.) 


BOOK    II. 
CHEMICAL    KINETICS. 

CHAPTER   I. 

DISSOCIATION. 

1 60.  WE   must   now   proceed  to  consider  some  of  the 
phenomena  which  are  connoted  by  the  term  chemical  kinetics. 
In  the  introduction  to  book  I.  I  said  that  this  term  is  to  be 
used  as  including  the  facts  and  principles  which  on  the  whole 
relate  to  chemical  action,  as  opposed  to  those  which  are  for 
the  most  part  connected   with   chemical    composition.     We 
have  however  seen  how   impossible  it  is  to  carry  out  this 
division  in  any  but  the  broadest  way.     We  have  seen  that 
the  same  facts  may  be,  indeed  must  be  viewed,  now   from 
the  statical,  now  from  the  kinetical  stand-point.     But  while 
this   is   true,   it   is,  I    think,  established   by   the   history   of 
chemistry  that  progress  has  been  made  at  some  periods  more 
by  seeking  knowledge  of  the  composition  than  of  the  reactions 
of  compounds,  while  at  other  times  inquiries  into  the  func- 
tions rather  than  the  composition  of  different  kinds  of  matter 
have  been  most  productive. 

A  chemical  change  must  be  looked  at  from  two  points  of 
view ;  the  relations  between  the  reacting  bodies,  and  the 
relations  between  the  forces  concerned  in  the  change,  must 
be  studied. 

161.  The  reactions  of  elements  and  compounds  when  pro- 
duced in  contact  with  oth;Qr  substances  furnish  problems  for 

M.  C.  23 


354  CHEMICAL  KINETICS.  [§  162 

the  solution  of  which  both  statical  and  kinetical  methods  are 
required.  Such  reactions  have  been  considered1  from  the 
point  of  view  of  the  composition  of  the  changing  system,  and 
some  of  them  have  been  also  regarded  from  the  stand-point  of 
thermal  chemistry2.  Emphasis  was  laid  on  the  necessity  of 
considering  not  only  the  composition  of  the  whole  changing 
system,  but  also  the  conditions  under  which  the  change 
proceeds,  e.g.  the  relative  masses  of  the  reacting  substances, 
the  rate  of  evolution  of  the  '  nascent '  products,  the  tempera- 
ture, &c. 

162.  The  fifth  section  of  the  second  chapter  of  book  I.  is 
occupied  with  questions  which  cannot  be  even  approximately 
answered  '  except  by  the  help  of  essentially  kinetical  con- 
ceptions. We  there  learned  to  recognise  the  existence  of 
substances  intermediate  between  true  compounds, — the  pro- 
perties of  which  are  for  the  most  part  conditioned  by  the 
nature,  number,  and  mutual  interactions  of  the  atoms  which 
compose  their  molecules, — and  true  mixtures, — the  properties 
of  which  are  the  means  of  those  of  their  constituents.  But 
the  consideration  of  c  molecular  compounds '  led  us  to  regard 
the  chemical  system  of  which  such  compounds  form  a  part  as 
continually  undergoing  change,  and  as  held  in  equilibrium,  as 
a  whole,  only  by  the  mutual  actions  and  reactions  of  its  parts. 
In  that  section  (par.  101)  facts  were  stated  which  seemed  to 
shew  that  molecules  of  different  degrees  of  complexity  may 
be  simultaneously  present  in  a  gas.  We  found,  for  instance, 
(par.  101)  that  the  gas  obtained  by  heating  phosphorus  penta- 
chloride  contains  molecules  of  PC13  and  C12  in  addition  to 
molecules  of  PC15 ;  and  that  as  temperature  rises  the  former 
kinds  of  molecules  increase  in  number,  while  the  latter 
decrease,  until  at  a  little  above  300°  no  PC15  molecules  remain. 
The  most  simple  and  probable  explanation  of  the  numbers 
representing  the  vapour  density  of  acetic  acid  at  different  tem- 
peratures and  pressures  is,  that  at  temperatures  below  120° 
(pressure  being  normal)  the  gas 'consists  for  the  most  part  of 
molecules  having  the  composition  C3H6O3,  but  that  at  250°  or 

1  Book  i.  chap.  n.  Section  1. 

2  Book  I.  chap.  iv.  pars.  122 — 124. 


§  163]  DISSOCIATION.  355 

so  (pressure  being  unchanged)  the  formula  CaH4O2  represents 
the  composition  of  by  far  the  greater  number  of  molecules 
which  compose  the  gas.  The  explanation  which  was  given  of 
these  and  similar  facts  regarding  the  relations  of  the  densities 
of  gases  to  temperature  and  pressure  was  based  on  the  kinetic 
theory  of  gases  (see  par.  101,  pp.  207 — 8).  If  that  explana- 
tion is  accepted,  it  follows,  I  think,  that  the  condition  of  a 
gas  in  which  dissociation  is  proceeding  must  be  such  that  the 
equilibrium  momentarily  established  between  molecules  of 
different  atomic  composition  is  being  continually  disturbed, 
and  fresh  conditions  of  equilibrium  are  being  established, 
which  in  turn  last  only  for  a  very  short  time 1. 

In  this  gradual  change  of  one  kind  of  molecules  into 
another  kind  brought  about  by  the  action  of  heat  we  have 
one  of  the  distinctive  features  of  dissociation,  or  thermolysis, 
the  phenomena  of  which  it  is  the  object  of  the  present  chapter 
to  examine2. 

163.  The  term  dissociation  is  generally  used  to  indicate  the 
resolution  of  more  into  less  complex  molecules,  by  the  action 
of  heat ;  the  amount  of  resolution  increasing  as  the  tempera- 
ture increases,  and  decreasing  when  the  temperature  decreases. 
For  each  substance  there  is  a  temperature  at  which  the  whole, 
or  almost  the  whole,  is  converted  into  two  or  more  new 

1  It  has  been  asserted  (Deville  and  Troost,  Compt.  rend.  64.  237  :  91.  54 ; 
Berthelot,  do.  91.  77)  that  the  observed  changes  in  the  densities  of  various  gases, 
e.g.  N2O4,  I2,  £c.,  at  different  temperatures  are  to  be  regarded  as  indicative  of 
variations  in  the  coefficients  of  expansion  of  these  gases.     If  this  is  so,  then  the 
relations  between  the  volumes  of  those  gases  and  the  temperature  are  very  curious. 
The  values  of  the  coefficients  of  expansion  of  those  gases  which  are  generally 
supposed  to  dissociate  when  heated,  must,  on  this  view,  be  regarded  as  increasing 
rapidly  with  increase  of  temperature  until  a  maximum  is  attained,  and  then  again 
decreasing  to  a  constant  value.   In  connection  with  this  subject  it  ought  to  be  remem- 
bered that  Gay-Lussac's  coefficient  of  expansion  (0*00365)  is  only  approximate, 
that  indeed  Boyle's  law  is  only  approximately  true,  but  that  at  the  same  time  the 
relation  between  the  volume  and  the  temperature  has  been  carefully  examined 
for  several  gases,   and  it  has  been    shewn    that    even  at    very   high    tempera- 
tures the  coefficients  of  expansion  of  these  gases  are  constant.     [The  gases  in 
question  are   H,  O,  N,  S,  Te,  Hg,  CO2,  HC1,  As4O6  ;    see  V.  Meyer,  Ber.  13. 

2O22.] 

2  In  connection  with  this  subject  generally  see  article  '  Dissociation '  in  Neues 
Handworterbuch  der  Chemie. 

23—2 


356  CHEMICAL   KINETICS.  [§  164 

bodies1.  If  the  temperature  is  now  allowed  to  fall,  the  pro- 
ducts of  the  original  change  gradually  recombine  until  the 
initial  state  of  the  system  is  again  attained.  When  on  the 
other  hand,  a  substance  undergoes  decomposition  by  the 
action  of  heat  there  is  a  certain  temperature-interval  within 
which  the  change,  if  started,  goes  to  completion  ;  moreover 
the  initial  state  is  not  regained  by  allowing  the  products  of 
the  change  to  cool  in  contact  with  each  other. 

When  a  substance  dissociates  at  least  one  of  the  products 
must  be  gaseous  under  the  conditions  of  the  experiment. 

1 64.  The  process  of  dissociation  presents  some  analogies 
with  that  of  evaporation.  In  both  there  is  a  gradual  change 
brought  about  by  the  action  of  heat.  As  the  rate  of  evapora- 
tion is  conditioned  by  the  pressure  exerted  on  the  liquid  by 
the  vapour,  so  the  rate  of  dissociation  is  conditioned  by  the 
sum  of  the  partial  pressures  of  the  gaseous  products  of  the 
action 2. 

For  any  temperature  there  is  a  certain  pressure,  such  that 
when  this  is  reached  the  process  stops,  but  it  may  be  again 
started  either  by  decreasing  the  pressure  or  by  increasing  the 
temperature.  This  pressure  has  been  called  the  dissociation  - 
pressure,  or  better  the  equilibrium-pressure.  Dissociation 
may  therefore  be  stopped  by  allowing  one  or  more  of  the 
gaseous  products  to  accumulate  in  contact  with  the  disso- 
ciating body  ;  on  the  other  hand  dissociation  may  be  caused 
to  proceed  rapidly  by  removing  one  or  more  of  the  gaseous 
products  as  quickly  as  it  is  produced. 

Thus  Wurtz  found  that  the  gas  obtained  by  vapourising 
phosphorus  pentachloride  into  an  atmosphere  of  phosphorus 
trichloride  was  composed  for  the  most  part  of  molecules  of 
PC15 ;  although  when  the  same  compound  was  vapourised  at 
the  same  temperature  into  air  the  molecules  of  PC15  were  for 

1  The  numbers  given  in  par.  101  for  the  densities  of  various  compounds  suffi- 
ciently represent  the  gradual  progress  of  dissociation-phenomena.     A  formula  is 
given  on  p.  204  (note)  by  means  of  which  the  amount  of  dissociation  of  gaseous 
compounds  may  be  calculated  from  observations   of  the   densities   at   different 
temperatures. 

2  See  especially  Deville,  Compt.  rend.  56.    195  ;   and  Lecons  sur  la  dissocia- 
tion. 


§§  1 65,  1 66]  DISSOCIATION.  357 

the  most  part  dissociated  into  PC13  and  Cl/.  So  also  Pebal2 
shewed  that  ammonium  chloride  may  be  permanently  decom- 
posed by  vapourising  it  in  an  arrangement  which  permits  of 
the  rapid  removal  of  the  less  dense  product  of  dissociation, 
although  when  the  same  compound  is  vapourised  into  an 
enclosed  space,  and  the  products  (ammonia  and  hydrochloric 
acid)  are  allowed  to  cool  in  contact  with  each  other,  the  whole 
of  the  original  substance  is  regained  in  the  solid  form. 

165.  When  solid  calcium  carbonate  is  heated  in  a  closed 
space  lime  and  carbonic  anhydride  are  formed,  but  on  cooling 
calcium  carbonate  is  reproduced. 

Debray3  has  shewn  that,  at  a  red  heat,  the  direction 
of  this  change  is  dependent  only  on  the  pressure.  For 
each  temperature  there  is  a  maximum  pressure  exerted  by 
the  gaseous  carbon  dioxide  at  which  the  direct  change, 
;rCaCO3  =  CaO  +  CO2  +  (r  -  i)  CaCO3,-  stops  ;  at  860°  this 
equilibrium-pressure  =81  m.m.  of  mercury  and  at  1000°  it  is 
equal  to  520  m.m.  If  a  system  consisting  of  CaO,  CaCO3,  and 
CO2  is  slowly  cooled,  the  whole  of  the  carbon  dioxide  is 
absorbed  by  the  lime,  but  if  the  temperature  is  rapidly  lowered 
some  of  the  dioxide  remains  uncombined  with  the  lime. 
If  the  temperature  is  slowly  lowered  a  certain  amount  of 
carbon  dioxide  is  absorbed,  the  pressure  is  changed,  and  the 
equilibrium  is  overthrown.  But  a  new  condition  of  equi- 
librium is  attained,  to  be  again  destroyed  by  absorption  of 
more  carbon  dioxide  following  on  a  further  lowering  of  tem- 
perature. Finally  stable  equilibrium  is  attained  when  the 
whole  of  the  dioxide  has  combined  with  the  lime.  If  how- 
ever the  temperature  is  caused  to  decrease  rapidly,  the  normal 
absorption  of  the  dioxide  corresponding  to  each  change  of 
temperature  cannot  be  completed,  and  the  cooled  system  is 
composed  of  chalk,  lime,  and  carbon  dioxide4. 

1 66.  Dissociation    is    thus    essentially  a   reversible   pro- 
cess5; it  is  accompanied  by  absorption  of  a  definite  quantity 


1  Conipt.  rend.  76.  601.  2  Annakn  123.  199. 

3  Co  nipt.  rend.  64.  603.  4  Fogg.  Ann.  149.  222. 

5  "A  physical  process  is  said  to  be  reversible,  when  the  material  system  can 


CHEMICAL  KINETICS.  [§  1 67 

of  heat  which  is  again  lost  by  the  system  as  it  passes  back  to 
its  original  configuration.  We  may  picture  to  ourselves  the 
action  of  heat  as  bringing  about  a  separation  of  the  molecules 
of  the  dissociating  body  into  atoms,  followed  by  a  rearrange- 
ment of  these  atoms  to  form  new  molecules,  the  new  system 
thus  produced  being  dependent  for  its  continued  existence 
on  supplies  of  energy  from  without  itself;  but  when  the 
supply  of  energy  in  the  form  of  heat  is  stopped,  we  may 
suppose  that  the  interatomic  attractions  bring  back  the 
system  to  its  original  molecular  arrangement.  When  how- 
ever a  chemical  decomposition  occurs  by  the  application  of 
heat,  the  new  configuration  assumed  by  the  atoms  is  stable,  it 
does  not  require  to  be  supplied  with  energy  from  without  in 
order  that  it  may  continue  to  exist ;  hence  there  is  no  swing- 
ing back  to  the  original  state. 

167.  In  the  dissociation  of  calcium  carbonate  the  system 
at  any  moment  is  composed  of  three  distinct  substances ;  a 
decrease  in  the  amount  of  calcium  carbonate  is  necessarily 
accompanied  by  an  increase  of  lime  and  carbonic  anhydride, 
and  vice  versa.  If  we  study  the  processes  of  dissociation 
wherein  more  than  one  arrangement  of  the  members  of  the 
system  is  possible,  we  shall  find  that  the  configuration 
assumed  at  any  given  temperature  depends,  as  in  the  simpler 
case  of  calcium  carbonate,  solely  on  the  pressure  exerted  by 
the  gaseous  products  of  the  change. 

Take,  for  instance,  the  two  compounds,  AgCl .  3NH3  and 
2AgC1.3NH3,  produced  by  the  action  of  ammonia  on  solid 
silver  chloride.  If  silver  chloride  is  brought  into  an  atmo- 
sphere of  ammonia,  at  ordinary  temperatures,  the  ammonia  is 
absorbed  with  formation  of  2AgCl .  3NH3,  and  the  pressure 
falls  ;  by  increasing  the  quantity  of  ammonia  absorption  again 
proceeds,  and  so  on.  For  every  temperature  there  is  a  certain 
pressure  whereat  neither  absorption  or  evolution  of  ammonia 
occurs ;  this  equilibrium-pressure  is  independent  of  the  relative 

be  made  to  return  from  the  final  state  to  the  original  state,  under  conditions 
which,  at  any  stage  of  the  reverse  process,  differ  only  infinitesimally  from  the  con- 
ditions at  the  corresponding  stage  of  the  direct  process."  Clerk  Maxwell ;  Article 
'  Diffusion '  in  Encycl.  Brit,  (pth  ed.). 


§  167]  DISSOCIATION.  359 

amounts  of  AgCl  and  2AgCl .  3NH3  present1.  When  the 
equilibrium-pressure  is  reached,  if  the  pressure  of  the  ammonia 
in  the  apparatus  is  largely  increased,  absorption  occurs  and 
the  compound  AgCl .  3NH3  is  produced.  For  this  compound 
also  there  is  a  pressure,  corresponding  to  each  degree  of 
temperature,  whereat  equilibrium  is  established.  The  follow- 
ing table  gives  some  of  the  equilibrium -pressures  as  deter- 
mined by  Horstmann2. 

Pressure  in  millimetres. 

Temp.             AgCl .  aNH3         2AgCl .  sNH3 
6°     22 

7  •'•  •••         23-4 

8  ...  432  ...  24*9 

9  ...  446  26-5 

10         465         28-2 

12          520  ...         ...  3i'9 

16          653        40-9 

18  ...  723  ...  46-6 

20          793        52-6 

The  difference  between  the  pressures  corresponding  to 
each  of  these  compounds  at  any  temperature  is  so  great  that 
it  is  comparatively  easy  to  study  the  relations  between  pres- 
sure, temperature,  and  amount  of  chemical  change  for  each 
compound :  but  when  attempts  are  made  to  do  this  for 
hydrated  salts,  e.g.  CuSO45H2O,  it  becomes  almost  impossible 
to  determine  the  equilibrium-pressures  for  various  tempera- 
tures. When  hydrated  copper  sulphate  is  heated  to  a  given 
temperature  in  an  enclosed  space  the  pressure  of  the  water- 
gas  evolved  shews  great  fluctuations.  At  first  sight  it  might 
be  thought  that  the  dissociation  of  this  salt  does  not  follow 
the  ordinary  rule,  viz.  that  the  equilibrium-pressure  is  in- 
dependent of  the  relative  amounts  of  decomposed  and  un- 
decomposed  solid  substances  present,  and  is  dependent  solely 
on  the  temperature.  But  on  closer  examination  it  is  found 
that  the  solid  undergoing  dissociation  is  really  a  mixture  of 
various  hydrated  salts,  each  with  its  own  equilibrium-pressure, 
but  that  the  differences  between  these  pressures  are  small.  In 

1  Horstmann,  Ber.  9.  749;  Isambert,  Compt,  rend.  66.  1259:  70.  456. 
~  loc.  cit. 


CHEMICAL  KINETICS.  [§  1 68 

this  case  we  have  therefore  a  number  of  processes  of  dis- 
sociation proceeding  simultaneously ;  hence  we  cannot  expect 
to  find  a  definite  equilibrium-pressure  for  each  temperature1. 

The  differences  between  the  equilibrium-pressures  of  the 
various  hydrates  are  so  marked  in  the  cases  of  some  hydrated 
salts,  that  the  phenomenon  of  dissociation  can  be  shewn  to 
follow  the  same  course  as  with  calcium  carbonate,  or  the 
ammoniacal  silver  chlorides2. 

168.  In  any  dissociating  system  at  the  equilibrium- 
pressure,  the  number  of  molecular  decompositions  and  re- 
compositions  must  be  regarded  as  equal  in  number  during 
any  given  interval  of  time.  A  general  theory  of  chemical 
change,  including  gaseous  dissociation,  based  on  the  molecular 
kinetic  theory  of  gases,  has  been  developed  by  Pfaundler. 
This  theory  will  be  considered  when  we  come  to  deal  in  detail 
with  the  subject  of  chemical  change3.  It  is  however  difficult 
to  reconcile  Pfaundler's  theory  with  the  fact  that  the  amount 
of  dissociation  of  a  solid,  into  solid  and  gaseous  products, 
is  independent  of  the  relative  quantities  of  the  original  sub- 
stance and  the  solid  product  of  dissociation.  In  the  dis- 
sociation of  calcium  carbonate,  e.g.  we  should  expect,  that  the 
greater  the  amount  of  lime  present,  relatively  to  the  amount 
of  carbonate,  the  greater  would  be  the  chances  that  some  of 
the  CO2  molecules  should  be  caught  and  held  fast,  and  that 
therefore  the  amount  of  dissociation  at  any  temperature 
would  depend  upon  the  ratio  between  the  lime  and  calcium 
carbonate  actually  present  in  the  system  at  that  temperature4. 
Pfaundler  has  very  ingeniously  tried  to  get  over  this  difficulty5 
by  referring  the  dissociation  only  to  the  molecules  on  the 
surfaces  of  the  various  members  of  the  system.  In  gases 
all  molecules  may  be  regarded  as  being  on  the  surface ;  but 

1  (See  Naumann,  Ber.  7.  1573.)      It  should  be  noted  that  the  equilibrium- 
pressure  for  a  given  temperature  is  never  attained  immediately  that  temperature  is 
reached ;  a  little  time  must  elapse  before  the  entire  system  has  settled  down  into 
equilibrium.     See  Horstmann,  Ber.  9.  752,  and  Naumann,  Annalen  160.  27. 

2  For  numbers  see  Debray,  Compt.  rend.  66.  194. 

3  See/cw/,  chap.  II.  par.  187. 

4  See  this  difficulty  stated  by  Horstmann,  Ber.  9.  757. 

5  Ber.  9.  1152. 


§  169]  DISSOCIATION.  361 

when  a  solid  is  present,  only  those  molecules  of  the  solid 
which  can  be  directly  bombarded  by  the  gaseous  molecules, 
are,  in  Pfaundler's  language,  on  the  surface.  The  number  of 
surface-molecules  is  very  small  compared  to  the  total  number, 
hence  a  change  in  the  relative  amounts  of  the  solid  com- 
pounds present  (call  these  AB  and  B)  will  be  accompanied  by 
a  change  in  the  ratio  of  surface-molecules  of  AB  to  those  of 

o 

B,  small  in  comparison  with  the  number  of  molecules  of  the 
gaseous  body  present  (call  this  A) ;  hence  only  a  small  change 
of  pressure  will  occur,  and  this  will  quickly  be  rectified  by 
the  absorption  (or  evolution)  of  a  little  more  of  A.  But  all 
molecules  of  A  must  gradually  come  to  the  surface  of  AB, 
and  take  part  in  the  exchange  which  is  going  on  between 
AB  and  A;  but  the  molecules  of  A  which  pass  into  the 
interior  of  the  solids  AB  and  B  will  remain  there  a  com- 
paratively long  time,  and  hence  will  exert  but  a  small  in- 
fluence on  the  pressure  of  the  gas  A. 

Horstmann1  has  rather  endeavoured  to  develop  a  general 
theory  of  dissociation  from  thermodynamical  principles ;  he 
has  deduced  a  formula  from  the  second  law  of  thermody- 
namics applicable  to  cases  of  dissociation,  and  generally  to 
chemical  changes  brought  about  by  the  action  of  heat,  and 
he  has  sought  to  shew  that  when  the  positive  and  negative 
changes  are  equal  in  a  process  of  dissociation,  i.e.  when  the 
equilibrium-pressure  is  reached,  the  entropy  of  the  system 
has  attained  its  maximum  value.  But  the  application  of 
thermodynamical  methods  to  questions  of  chemical  equi- 
librium, including  dissociation,  will  be  considered  in  another 
chapter. 

169.  The  special  characteristics  of  dissociation  which, 
taken  together,  mark  it  off  from  decomposition,  are  then 
briefly  these2:  (i)  heat  is  absorbed,  and  the  temperature  of 
the  dissociating  system  increases  throughout  the  entire  pro- 
cess ;  (2)  the  original  configuration  of  the  system  is  returned 
to,  if  the  products  of  dissociation  are  allowed  to  cool  in 
contact  with  each  other ;  (3)  the  change  is  gradual,  and 

1  Annalen  170.  192  ;  see  also  do.  Supplbd.  8.  112. 

2  See  Ncues  Handworterbuch  der  Cheniie,  2.  999. 


362  CHEMICAL  KINETICS.  [§  170 

therefore  at  any  given  temperature  the  dissociation  is  partial, 
although  the  whole  mass  of  the  dissociating  substance  is  sub- 
mitted to  the  same  thermal  conditions  as  regards  supply  of 
heat  from  without ;  (4)  the  amount  of  dissociation  is  dependent 
on  the  temperature  and  pressure  of  the  gaseous  product  or 
products;  and  (5)  is  independent  of  the  ratio  between  the 
quantities  of  the  solid  products  of  the  change  present  at  any 
temperature1. 

170.  It  is  evident  that  the  possible  occurrence  of  dis- 
sociation must  have  an  important  bearing  on  determinations 
of  the  densities  of  gaseous  compounds  from  which  the  mole- 
cular weights  of  these  compounds  are  deduced2. 

We  have  already  learned  (par.  101)  that  the  density  of  the 
vapour  of  acetic  acid  decreases,  as  temperature  increases, 
from  the  boiling  point  to  about  100°  above  this  point,  after 
which  it  becomes  constant.  If  the  temperature  is  kept  con- 
stant and  the  pressure  is  increased,  the  density  of  the  vapour 
increases.  The  rate  of  change  in  the  value  of  the  density  of 
this  vapour,  which  accompanies  change  of  temperature  and 
pressure,  is  much  more  rapid  than  the  rate  of  change  in  the 
value  of  the  density  of  air  under  similar  conditions ;  there  are 
however  no  abrupt  changes  in  the  value  under  discussion. 
The  smallest  molecular  formula  assignable  to  acetic  acid, 

1  It  is  probable  that  relatively  less  energy  is  transformed  into  heat  in  the 
formation  of  a  dissociable  compound  from  its  constituents,  than  in  the  formation  of 
an  analogous  compound  which  decomposes,  but  does  not  dissociate,  when  heated. 
If  this  is  so,  then  perhaps  the  relatively  small  evolution  of  heat  which  attends  the 
formation  of  the  former  compound  may  be  connected  with  the  existence  of  atomic 
groups  in  the  molecule  (or  in  the  reacting  unit)  of  this  compound.  When  the 
compound  is  heated,  it  separates,  on  this  supposition,  into  those  groups  the  parts 
of  which  hold  together ;  whereas  when  the  other  compound  is  heated  much 
energy  is  absorbed,  and  the  result  is  a  separation  of  the  molecules  into  their  con- 
stituent atoms,  which  at  once  pair  off  into  new  molecules,  so  that  the  conditions 
required  for  the  re-formation  of  the  original  compound  no  longer  exist.  This  view 
may,  I  think,  be  shewn  to  be  in  keeping  with  Pfaundler's  theory  of  chemical 
equilibrium  (see  post,  chap.  II.  par.  187).  The  ratio  of  the  energy  of  rotation  of 
the  parts  of  the  molecules  to  the  energy  of  agitation  of  the  molecules  as  wholes, 
would,  on  this  view,  be  partly  dependent  on  whether  these  molecules  were  built 
up  of  individual  atoms,  or  of  groups  of  atoms  each  of  which  was  more  thermally 
stable  than  the  molecules  themselves. 

3  See  ante,  book  I.  chap.  I.  par.  16. 


§  170]  DISSOCIATION.  363 

which  shall  express  its  percentage  composition  [C=I2,  O  =  i6, 
H=i],  is  H2CO;  the  other  possible  formulae  are  H4C2O2, 
H  C  O  ,  H  CO,  &c.,  &c.  Now  if  we  tabulate  the  observed 

(533^  844 

densities  of  acetic  acid  vapour  at  different  temperatures,  and 
compare  them  with  the  densities  of  the  hypothetical  com- 
pounds H2CO  &c.  we  have  this  result. 

Density  of  vapour  of  acetic  acid  at  760  mm. 

Temp.  Observed.  Calculated  for  formula. 

125°  3-20  C4H8O4=4'i5 

130  3-12  C3H6O3  =  3-n 

140  2-90  C2H4O2  =  2'o8 

150  275  CH2O  =  ro4 

1 60  2*48 

170  2-42 

190  2-30 

200  2*22 

220  2-17 

230  2'09 

250  2-o8 

300  2'o8 

The  progress  of  the  change  represented  by  the  varying 
value  of  the  density  is  very  gradual;  we  cannot  therefore 
suppose  that  each  temperature  on  the  table  is  marked  by  the 
presence  of  molecules  of  a  definite  weight,  and  by  the 
presence  of  these  molecules  only.  The  process  represented 
by  these  numbers  is  analogous  to  the  processes  of  dissociation 
which  we  have  considered  ;  the  explanation  in  terms  of  the 
kinetic  theory  of  gases  has  already  been  given  (par.  101,  pp. 
207 — 8),  and  has,  I  think,  been  shewn  to  be  fairly  satisfactory1. 
If  that  explanation  is  accepted  it  follows  that  the  density  of 
any  chemically  homogeneous  vapour  obtained  by  heating  a 
liquid  substance  should  not  attain  a  constant  value  until  the 
gas  has  been  raised  some  degrees  above  the  boiling  point  of 
the  liquid.  The  temperature-interval  through  which  the  gas 
must  be  raised  will  vary,  according  to  the  nature  of  the  gas, 
and  of  the  liquid  from  which  it  is  obtained.  This  theoretical 
deduction  has  been  verified  by  experiments  so  far  as  these 

1  See  in  connection  with  this  subject  O.  E.  Meyer's  Die  Kinetische  Theorie  der 
Case,  pp.  76 — 82. 


364  CHEMICAL   KINETICS.  [§  1 70 

have  yet  extended1.  Numbers  have  been  given  (par.  101, 
p.  209)  which  shew  that  constant  values  are  obtained  for  the 
densities  of  the  easily  gasifiable  elements  chlorine  and  bro- 
mine, only  at  150°  or  200°  above  the  boiling  points  of  these 
bodies. 

The  numbers  representing  the  density  of  the  gas  obtained 
by  heating  phosphorus  pentachloride  which  are  given  in  par. 
101  (p.  204)  shew,  that  even  at  about  30°  above  the  boiling 
point  of  this  compound  the  observed  density  is  approximately 
30  per  cent,  less  than  that  calculated  from  the  formula  PC15. 
Wurtz2  diffused  the  vapour  of  this  compound,  at  temperatures 
a  little  below  its  boiling  point,  into  a  flask  containing  air  ;  by 
determining  the  weight  of  the  mixed  gases  (air  and  vapour  of 
phosphorus  pentachloride)  and  the  volume  of  each,  it  was 
possible  to  calculate  the  partial  pressure  to  which  the  latter 
was  subjected.  Some  of  Wurtz's  results  are  given  in  tabular 
form;  the  volumes  are  stated  in  cc.  and  are  reduced  to  o° 
and  760  mm. 

Temperature        Volume  of  vapour  Density  of  vapour  Partial 

of  experiment.         of  pentachloride.         Volume  of  air.  of  pentachloride.          pressure. 

145°  85-1  123-0  670  311  mm. 

137  3975  165-15  6-47  148     „ 

129  52-8  179-0  6-63  170    „ 

The  density  of  the  gas  obtained  by  vapourising  phosphorus 
pentachloride  under  these  conditions  is  only  about  8  per  cent, 
less  than  that  required  by  the  formula  PC15. 

Wurtz  then  diffused  the  vapour  of  the  pentachloride  into 
a  flask  containing  a  known  amount  of  phosphorus  trichloride 
vapour  ;  from  the  sum  of  the  weights  of  the  two  gases,  and 
from  analyses  of  the  contents  of  the  flask,  he  was  able  to 
calculate  the  volume  and  weight  of  the  vapour  from  the 
pentachloride,  and  the  pressure  to  which  that  vapour  was 
subjected  in  the  flask.  As  the  mean  of  12  experiments,  at 
temperatures  ranging  from  160°  to  175°,  and  pressures  varying 
from  168  to  413  mm.,  Wurtz  obtained  the  number  7-23  as 
representing  the  density  of  the  vapour  of  phosphorus  penta- 

1  See,  for  illustrations,  Naumann's  Thermochemie,  pp.  155 — 8. 
'2  Coinpt.  rend.  76.  60 1. 


§  170]  DISSOCIATION.  365 

chloride,  obtained  by  gasifying  this  substance  into  an  atmo- 
sphere of  phosphorus  trichloride. 

Hence  there  seems  to  be  little  doubt  that  the  so-called 
anomalous  vapour  density  of  phosphorus  pentachloride  is 
indicative  of  the  dissociation  of  molecules  of  PC15  into  mole- 
cules of  PC13  and  C12. 

There  has  been  a  great  deal  of  discussion  within  recent 
years  as  to  the  action  of  heat  on  chloral  hydrate.  Does  the 
vapour  obtained  by  heating  this  substance  contain  chloral 
and  water,  or  is  it  composed  of  chloral  hydrate  ?  The  follow- 
ing results  were  obtained  by  Naumann  \ 

Density 


Observed  Calculated  for 

Temp.  Pressure.  'cCL,.  COH+H2O        CC13.CH(OHJ 

100°          450-5  mm.  2-81 

78-5         162      „  2-83 

Hence  chloral  hydrate  appears  to  undergo  complete  disso- 
ciation into  chloral  and  water  at  78°,  and  under  so  small  a 
pressure  as  162  mm. 

These  numbers  were  not  accepted  by  Troost,  Berthelot, 
and  others,  as  conclusive,  because  these  chemists  are  opposed 
to  the  conceptions  of  modern  chemistry  which  are  founded  on 
the  distinction  between  atoms  and  molecules.  As  this  distinc- 
tion is  an  outcome  of  the  application  of  Avogadro's  law  to 
chemical  processes,  it  is  evident  that,  could  this  law  be  over- 
thrown, the  distinction  in  question  would  appear  to  be  less 
well  grounded.  Now  if  it  could  be  proved  that  the  density  of 
a  homogeneous  gas  is  only  half  as  great  as  the  number 
calculated  by  the  use  of  Avogadro's  law,  an  important  step 
would  be  made  towards  overthrowing  the  law  in  question. 

It  has  been  shewn  that  the  vapour  obtained  by  heating 
chloral  hydrate  diffuses  as  a  mixture  of  chloral  vapour  and 
water  and  not  as  a  homogeneous  gas2;  further  that  chloral 
vapour  is  not  hydrated  in  the  vapour  obtained  by  heating 
chloral  hydrate,  provided  the  pressure  of  the  former  is  greater 

1  Ber.  9.  822. 

2  Wiedemann  and  Schulze,    Wicd.  Ann.  6.  -293. 


366  CHEMICAL  KINETICS.  [§  I /I 

than  the  equilibrium-pressure  of  the  latter  at  the  temperature 
of  experiment1;  and  also  that  the  vapour  in  question  behaves 
towards  a  hydrated  or  dehydrated  salt  in  the  same  way  as  a 
gaseous  mixture  containing  water2.  Moreover  Engel  and 
Moitessier3  have  shewn  that  when  chloral  hydrate  is  distilled 
with  chloroform  at  60°,  the  distillate  contains  both  water  and 
chloral.  Naumann  has  also  proved  that  when  chloral  hydrate 
is  distilled  alone,  the  distillate  contains  much  chloral  and  a 
little  water,  and  the  residue  much  water  and  a  little  chloral4. 
Finally  the  densities  of  the  gases  obtained  by  heating  chloral- 
alcoholate5  and  butylchloralhydrate 6  shew  that  these  com- 
pounds, which  are  analogous  to  chloral  hydrate  both  in 
composition  and  function,  undergo  dissociation  when  heated. 
Hence  there  can  be  no  doubt  that  the  compound  CC13.CH(OH)2 
is  dissociated,  even  at  low  temperatures  and  small  pressures, 
intoCQ3.COH  +  Ha07. 

171.  The  characteristic  features  of  dissociation,  as  con- 
trasted with  decomposition,  have  already  been  summarised 
(par.  169).  It  is  not  possible  however  to  define  the  term 
dissociation.  There  are  many  changes  which  present  more 
or  less  close  resemblances  to  well-marked  processes  of  dis- 
sociation. Sometimes  the  resemblance  is  so  close  that  we 
have  little  hesitation  in  classing  the  actions  under  the  heading 
of  dissociation ;  sometimes  it  is  impossible  to  place  the 
phenomenon  entirely  in  the  class  of  dissociation  or  in  that  of 
decomposition.  Thus  when  hydrogen  and  water-vapour  are 
passed  over  a  mixture  of  iron  and  magnetic  oxide  of  iron,  it 
is  found  that  a  state  of  equilibrium  is  maintained  for  any 
given  temperature,  and  that  this  equilibrium  is  independent 
of  the  relative  quantities  of  the  two  solids  present,  and  is  con- 
ditioned only  by  the  pressures  of  the  water-vapour  and 

1  Naumann,  Thermochemie,  136. 

2  Wurtz,  Compt.  rend.  84.  977:  86.  1170:  90.  118,  337,  572. 

3  Compt.  rend.  88.  285  :  90.  97. 

4  Ber.  12.  738. 

5  Wurtz,  Compt.  rend.  85.  49. 

6  Engel  and  Moitessier,  Compt.  rend.  90.  1075. 

7  For  a  fuller  discussion  of  the  dissociation  of  chloralhydrate,  see  Naumann's 
Thermochemie ',  134 — 137. 


§  172]  DISSOCIATION.  367 

hydrogen,  which  pressures  are  always  in  the  same  ratio  to 
each  other  as  long  as  the  temperature  remains  unchanged1. 

Although  there  is  here  a  more  complex  series  of  changes 
than  in  the  cases  of  dissociation  hitherto  studied,  yet  because 
the  change  is  brought  about  by  raising  the  temperature, 
because  the  amount  and  direction  of  the  change  are  depend- 
ent only  on  the  temperature  and  the  pressure  of  the  gaseous 
components  of  the  changing  system,  and  because  the  change 
is  reversible,  we  are  entitled  to  class  the  reaction  in  question 
as  a  dissociation -phenomenon. 

172.  It  has  been  experimentally  proved  that  many  salts — 
e.g.  ammonium  salts,  many  of  the  alums,  cobalt  chloride, 
sodium  sulphate,  &c. — are  partially  resolved  into  their  con- 
stituents when  dissolved  in  much  water.  Further,  it  has  been 
shewn  that  the  amount  of  this  decomposition  is  dependent  on 
the  temperature  and  the  relative  masses  of  water  and  salt ; 
and  finally  that  the  change  can  be,  at  least  partially,  reversed 
by  lowering  the  temperature  of  the  solutions2. 

The  action  of  the  water  in  these  changes  has  been  com- 
pared to  the  action  of  the  pressure  of  the  gases  produced  in  a 
process  of  dissociation.  Dilution  may  thus  be  regarded  as  ana- 
logous to  decreased  pressure.  But  the  analogy  is  misleading. 
In  many  if  not  all  cases  of  so-called  dissociation  in  solution, 
water  is  itself  one  of  the  components  of  the  original  sub- 
stance ;  hence,  judging  from  the  analogy  of  gaseous  dis- 
sociation, we  should  expect  that  as  this  product  of  the  change 
accumulates  the  process  would  become  slower  and  would 
eventually  stop.  But  we  find  that  increasing  the  quantity 
of  water  acts  in  the  same  way  as  decreasing  gaseous  pressure. 
The  water  probably  exerts  two  actions ;  one,  which  may  be 
called  physical,  whereby  an  increase  in  the  quantity  of  water 
gives  greater  freedom  of  motion  to  the  particles  of  the  dis- 
solved substance,  and  also  lessens  the  chances  of  combination 
between  the  separated  components  of  this  substance;  and 

1  Deville,  Compt.  rend.  70.  1105  :  71.  30. 

2  Examples  will  be  found  in  Watts's  Diet.  Supplt.  2.  292  et  seq.     See  also  for 
the  case  of  iron  sulphate,  chloride  and  nitrate,  G.  Wiedemann,  Pogg.  Ann.  126. 
i  :  135.  177. 


368  CHEMICAL   KINETICS.  [§  172 

one,  which  may  be  called  chemical,  whereby  any  increase  in 
the  quantity  of  water  brings  about  the  formation  or  decom- 
position of  definite  compounds  which  would  not  otherwise  be 
produced.  While  an  increase  in  the  quantity  of  water  may, 
in  one  respect,  tend  to  increase  the  amount  of  chemical 
change,  it  may,  in  the  other  respect,  exert  an  opposite  in- 
influence.  When  the  first  of  these  actions  of  water  is  much 
more  marked  than  the  second  we  shall  have  phenomena 
occurring  which  closely  resemble  those  presented  in  gaseous 
dissociation1. 

The  influence  exerted  by  varying  the  relative  mass  of  the 
water  present  in  such  a  process  as  the  separation  of  ferric 
chloride  into  hydrochloric  acid  and  soluble  ferric  hydroxide, 
suggests  that  certain  classes  of  compounds,  more  especially 
such  as  contain  water  as  one  of  their  constituents,  may  be 
able  to  exist  in  the  presence  of  water,  although  when  the 
water  is  removed  they  separate  into  their  constituent  parts. 
This  subject  cannot  however  be  considered  until  we  have 
gained  more  knowledge  of  the  conditions  which  affect  the 
equilibrium  of  chemical  systems2. 

1  For  the  fuller  illustration  and  discussion  of  'dissociation  in  solution,'  see 
Naumann's  Thermochemie,  158 — 167;  and  article  'Dissociation'  in  Neues  Hand* 
worterbuch  der  Chemie,  especially  pp.  999 — 1002. 

2  See/tatf,  par.  18?. 


CHAPTER   II. 

CHEMICAL    CHANGE. 

SECTION  I.     General  Considerations. 

173.  PROCESSES  of  dissociation  present  examples  of 
chemical  systems  maintained  in  equilibrium  by  the  opposing 
actions  of  various  forces.  We  have  repeatedly  had  occasion 
to  employ  this  conception  in  a  general  way  in  preceding 
chapters  ;  it  remains  now  that  we  endeavour  to  make  it  some- 
what more  definite. 

Many  of  the  older  chemists  were  accustomed  to  regard 
chemical  change  as  a  continuous  process ;  among  those  who 
made  this  conception  prominent  Berthollet  and  Davy  are 
especially  to  be  mentioned. 

The  early  years  of  the  present  century  are  most  important 
in  the  history  of  chemistry :  in  1 808  appeared  Dalton's  New 
System;  in  1803  Berthollet  published  his  Essai  de  Statique 
Chimique. 

Berthollet  sought  to  explain  chemical  action  as  the  result 
of  attractions  between  the  small  particles  of  which  bodies  are 
composed1.  These  attractions  are,  he  said,  probably  of  the 
same  kind  as  those  between  large  masses  of  bodies ;  in  the 
latter  cases  we  speak  of  the  attraction  of  gravity,  in  the  former 
of  the  attraction  of  affinity.  This  attraction  between  the 
small  particles  of  bodies,  when  conditions  are  favourable, 
results  first  in  cohesion,  and  then  in  combination.  But  other 
forces  may  come  into  play  the  results  of  which  are  opposed 
to  those  of  the  attraction  of  affinity ;  heat  may  cause  the 

1  See/atf,  chap.  in.  par.  200. 
M.  C.  24 


3/0  CHEMICAL  KINETICS.  [§  173 

expansion  of  substances  which  would  otherwise  combine ; 
solution  may  weaken,  or  destroy,  the  cohesion  of  the 
particles  of  a  solid.  Whether  combination  occur  or  not,  and 
if  it  occur,  whether  the  products  remain  unchanged  or  not, 
depends,  on  Berthollet's  view,  upon  the  relative  magnitudes  of 
the  opposing  forces.  If  the  attraction  between  the  particles 
of  different  kinds  of  matter  is  greater  than  the  action  of  the 
forces  which  tend  to  separate  these  particles,  then  a  new 
compound,  or  compounds,  will  be  formed.  Should  these 
compounds  be  solids  under  the  experimental  conditions,  the 
cohesion  of  their  particles  will  act  in  the  same  direction  as 
the  attraction  of  affinity  which  is  the  immediate  agent  in 
their  production.  The  final  arrangement  of  the  particles  of 
two  kinds  of  matter  depends,  according  to  Berthollet,  not 
only  on  the  relative  magnitudes  of  the  different  attractions 
between  them,  but  also  on  the  relative  masses  of  the  re- 
acting bodies ;  thus  a  relatively  small  attraction  may  be  made 
to  overcome  a  greater,  by  largely  increasing  the  mass  of  one 
of  the  two  kinds  of  matter. 

Berthollet  regarded  a  liquid  holding  a  solid  in  solution  as 
a  system  in  a  state  of  more  or  less  unstable  equilibrium ;  by 
removing  some  of  the  liquid  by  evaporation,  or  by  lowering 
the  temperature,  or  in  other  ways,  this  equilibrium  might  be 
overthrown,  and  crystals  would  separate,  containing  particles 
both  of  the  solid  previously  in  solution,  and  also  of  water 
changed  from  the  liquid  to  the  solid  state.  Such  a  system, 
said  Berthollet,  will  present  two  extreme  cases,  (i)  all  the 
solid  is  held  in  solution  by  the  liquid,  (2)  all  the  liquid  is 
changed  to  the  state  of  solid.  Between  these  extremes  there 
may  be  many  states  each  marked  by  a  certain  relation 
between  the  amounts  of  solid  and  liquid  compounds;  for 
Berthollet  regarded  the  solution,  no  less  than  the  crystals 
which  separated,  as  a  compound,  or  a  series  of  compounds,  of 
water  and  salt. 

Combination  and  solution  were  looked  on  by  Berthollet 
as  analogous  actions.  'In  solution/  he  said,  'one  pays 
'attention  chiefly  to  the  liquidity  acquired  by  the  solid  by 
'combining  [with  the  solvent],  and  especially  to  the  uni- 


§  173]  CHEMICAL  CHANGE.  371 

'formity  of  the  parts  of  the  liquid  compound.... In  a  com- 
'  bination  one  principally  considers  the  other  properties  of  the 
'compound  which  is  produced,  comparing  therewith  the 
1  properties  of  the  substances  which  produced  it.  In  most 
'cases  solution  is  due  to  a  combination  so  feeble  that  the 
'  properties  of  the  dissolved  substance  do  not  disappear1.' 

Again  '  chemical  action  is  reciprocal ;  its  effect  is  the 
'  result  of  a  mutual  tendency  to  combination.  One  ought  not, 
'strictly  speaking,  to  say  that  a  liquid  acts  upon  a  solid, 
'  rather  than  that  the  solid  acts  upon  the  liquid  ;  it  is  more 
'convenient  however  to  ascribe  the  whole  of  the  action  to 
'  one  of  the  substances,  when  one  wishes  to  examine  the  pro- 
'  ducts  of  the  action,  rather  than  the  action  itself2.' 

When  lime  is  placed  in  water,  mutual  action,  said  Berthollet, 
begins  at  once,  but  the  cohesion  of  the  particles  of  the  solid 
is  so  great  that  the  dissolving  action  of  the  water  does  not 
produce  any  marked  effect  for  some  time ;  but  water  is  being 
absorbed  by  the  lime,  and  thus  the  effect  of  the  cohesion  of 
the  particles  of  the  lime  is  slowly  overcome  by  that  of  the 
solvent  action  of  the  water,  until  finally  the  lime  dissolves. 
During  this  process  two  combinations  of  lime  and  water  are 
formed,  one  solid,  the  other  liquid ;  the  effect  of  one  force, 
cohesion,  is  to  increase  the  amount  of  the  former ;  the  effect 
of  another  force,  solution,  is  to  increase  the  amount  of  the 
latter  combination.  A  state  of  equilibrium  is  established, 
and  continues  so  long  as  the  conditions  are  unchanged ; 
but  alteration  of  temperature,  or  changes  in  the  relative 
masses  of  water  and  lime,  suffice  to  overthrow  this. equilibrium 
and  to  establish  another3. 

Berthollet  not  only  formed  a  clear  mental  image  of  a 
system  as  held  in  equilibrium  by  the  actions  and  reactions  of 
its  various  constituents,  but  he  also  had  what  I  think  must  be 
regarded  as  a  very  clear  conception  of  the  chief  forces  con- 
cerned in  maintaining  this  equilibrium.  In  the  summary  to 
Part  I.  of  the  Essai,  he  says :  '  The  chemical  qualities  of 

1  Essat,  1.  59 — 60.  2  Essai,  1.  36 — 37. 

3  Essat,  1.  37.     A  theory  of  solution,  closely  resembling  that  of  Berthollet, 
has  been  proposed  by  W.  W.  J.  Nicol :  see  Phil.  Mag.  (5)  15.  91. 

24—2 


372  CHEMICAL  KINETICS.  [§  174 

different  substances  depend  (i)  on  their  tendencies  to  com- 
'  bine,  whereby  they  mutually  saturate  each  other,  and  which 
'  tendencies  remain  more  or  less  dominant  in  the  compounds 
*  produced ;  (2)  on  their  relations  to  heat,  which  modify  their 
'  combining  powers,  by  causing  variations  in  the  quantities  of 
'  the  substances  coming  within  the  spheres  of  mutual  action, 
'and  also  by  opposing  elasticity  (elasticity  to  condensation, 
'the  latter  of  which  is  one  of  the  effects  of  combination  ;  (3) 
'on  the  mutual  actions  of  their  small  particles  (molecules*} , 
'  acting  in  the  same  direction  as  the  affinity  which  has  pro- 
'duced  combination,  but  opposed  to  actions  and  reactions 
'  between  these  particles  and  those  of  other  substances ;  (4) 
'on  their  relations  to  other  substances,  which  combine  with 
'  them,  but  not  so  as  to  produce  a  mutual  saturation  (satura- 
'  tion*),  but  rather  a  division  and  varying  distribution  of 
'  properties,  and  chiefly  of  those  properties  which  depend  on 
'  the  constitution  (constitution4')! 

174.  Davy,  as  we  found  in  book  I.  (chapter  II.  par.  46), 
regarded  chemical  and  electrical  effects  as  probably  due 
to  the  same  cause,  certain  mutual  relations  between  small 
particles  of  matter  producing  effects  called  chemical,  as  certain 
mutual  relation  between  masses  of  matter  produce  effects 
called  electrical.  Davy  regarded  a  fixed  chemical  system  as 
stable  because  of  the  balance  of  chemical  and  electrical  forces ; 
'  contact  of  the  metals  [in  the  galvanic  pile]  destroys  electrical 
'  equilibrium,  and  chemical  changes  restore  it  again,  and  in 
'consequence  the  action  [of  the  pile]  exists  as  long  as  the 
4  decompositions  continue.' 

1  £lasticite.     Berthollet  uses  this  word  as  meaning  nearly  the  same  as  dilata- 
tion, or  perhaps  we  might  now  say  disgregation.    (See  chap.  in.  par.  239,  foot-note.} 

2  Molecules.    This  word  as  employed  by  Berthollet  means  only  a  small  particle ; 
I  have  thought  it  better  not  to  use  the  term  molecule,  as  this  is  now  employed  with 
a  more  definite  meaning  than  small  particle. 

3  Saturation.     By  saturation  of  properties  Berthollet  means  that  merging  of 
the  properties  of  the  constituents  in  those  of  the  new  compound  which  is  so 
characteristic  of  chemical  change. 

4  Constitution.     The  constitution  of  a  substance  is  conditioned  according  to 
Berthollet  by  its  condensation  and  dilatation  :  '  the  properties  which  depend  on 
the  constitution '  of  a  substance  may  be  taken  as  meaning,  broadly,  the  physical 
properties  of  the  substance, 


§§  I75>  176]  CHEMICAL  CHANGE.  373 

175.  The  picture  of  a  chemical  reaction  which  Berzelius 
formed  for  himself  was  essentially  based  on  the  conception 
of  equilibrium  resulting  from  the  actions  and  reactions   of 
chemical  and  electrical  forces.     Each  elementary  atom  was, 
for  him,   endowed  with  definite   quantities   of  positive   and 
negative  electricity,  but  each  atom  was  nevertheless  essentially 
unipolar.     The  strivings  of  atoms  to  neutralize  their  opposite 
electricities  is  measured  by  the  intensity  of  the  unipolarity  of 
each.    This  striving  is  what  Berzelius  called  chemical  affinity. 

These  great  chemists  were  agreed  in  regarding  the  object 
of  chemistry  to  be  an  explanation  of  'the  changes  which 
matter  undergoes ;  they  did  not  think  that  the  ability  to  give 
an  account  of  the  physical  properties  of  each  kind  of  matter 
sufficed  to  make  one  a  chemist.  Chemical  change  was,  for 
them,  continuously  proceeding,  but  it  might  be  checked  by 
the  action  of  electrical,  or  thermal,  or  other  forces.  Their 
fundamental  conception  is  clearly  that  of  an  equilibrium 
resulting  from  the  actions  of  different  forces,  the  principal  of 
which  are  chemical,  electrical,  and  thermal. 

176.  Little  was  done  to  advance  the  study  of  chemical 
change  until  comparatively  recent  times.     In  1867  Guldberg 
and  Waage  published  their  most  important  memoir  Etudes 
sur  les  Affinites  Chimiques.     These  naturalists,  whose  work 
we    must    study   carefully   in    another   chapter,   have    paid 
attention  chiefly  to  changes  which  are  reversible  and  which 
belong  to  the  general  type  represented  by  the  two  equations1: 

(1)  AB+CD=AC+BD, 

(2)  AC+BD=AB+CD. 

The  cycle  consists  of  two  parts,  (i)  the  direct  change,  (2) 
the  reverse  change;  it  presents  analogies  with  dissociation2. 

1  An  instance  of  such  a  reversible  change  is  furnished  by  the  action  of  alcohols 
on  acids, 

ROH+R'COOH  =  R'COOR  +  HOH  :  R'COOR  +  HOH  =  ROH  +  R'COOH. 
Van't  Hoff  proposes  the  notation 

AB  +  CD  ^ZI±  AC  +  BD 
for  reversible  changes.     (Etudes  de  Dynamique  Chimique  [1884],  p.  8.) 

2  See  ante,  pars.  171,  172. 


374  CHEMICAL  KINETICS.  [§§  1 77,  178 

If  AH,  CD,  AC,  and  BD  are  all  in  the  same  physical  state, 
say  are  all  gases,  the  direction  and  amount  of  the  change  will 
be  chiefly  conditioned  by  chemical  forces ;  but  if  one  of  these 
bodies  is  a  solid  or  liquid,  if  one  is  more  insoluble  in  the 
menstruum  present  than  the  others,  if  one  is  more  compact 
than  the  others,  &c.,  then  the  amount  and  direction  of  the 
change  will  be  more  or  less  conditioned  by  what  Guldberg  and 
Waage  call  secondary  forces.  One  principal  object  of  the 
Etudes  is  to  eliminate  the  influence  of  secondary  forces,  and 
so  to  arrive  at  relative  measurements  of  the  chemical  forces 
which  condition  chemical  changes,  in  other  words,  to  gain 
relative  measurements  of  chemical  affinities. 

177.  But  we  are  not  yet  in  a  position  to  discuss  the  work 
of  the  Norwegian  naturalists  from  this  point  of  view.     At 
present  we  are  endeavouring  to  gain  a  general  view  of  the 
conditions  and  the  course  of  chemical  actions.     Now  there 
are  many  groups  of  facts  which  must  some  day  find  their 
place  in  a  general  theory  of  chemical  action,  but  which  lie 
scattered,  in  a  more  or  less  casual  way,  over  the  pages  of 
chemical  memoirs;    the  more  important  of  these  facts  may 
be  roughly  classified  under  the    following  four   heads:    (i) 
contact-actions ;  (2)  predisposing  affinity ;  (3)  induction ;  (4) 
influence  of  mass. 

I  wish  now  to  illustrate  each  of  these  groups  of  facts. 

178.  Contact-actions^.  When  a  mixture  of  sulphur  dioxide 
and  oxygen  is  passed  over  hot  finely-divided  platinum  the 
gases  combine  to  form  sulphur  trioxide,  but  the  platinum  is 
unchanged  at  the  end  of  the  reaction.     Ozone  is  decomposed 
by  contact  with  metallic  silver,  while  the  silver  is  itself  un- 
changed.    When  acetylene  is  heated  in  a  closed  tube  over 
mercury  it  is  gradually  changed  into  a  mixture  of  benzene, 
cinnamene,  naphthalene,  &c.,  but  if  a  piece  of  recently  heated 
coke   is    introduced   into   the  tube,  the  acetylene  is  almost 
wholly  changed  into  carbon  and  hydrogen,  while   the  coke 
is  itself  unaffected2.     When  sulphur  dioxide  and  chlorine  are 
passed  into  a  little  camphor,  much  sulphuryl  chloride  (SO2C12) 

1  Called  also  catalytic  actions. 

8  Armstrong  and  Groves,  Organic  Chemistry,  211  (quoting  Berthelot). 


§  178]  CHEMICAL  CHANGE.  375 

is  produced,  and  the  camphor  is  unchanged  at  the  close  of 
the  action ;  but  chlorine  has  no  action  on  liquid  sulphur 
dioxide,  nor  does  it  act  upon  camphor  under  the  conditions 
which  exist  in  the  formation  of  sulphuryl  chloride.  Some 
other  substances  which  absorb  sulphur  dioxide,  e.g.  alcohol, 
acetone,  sulphur  trioxide,  &c.,  do  not  bring  about  the 
formation  of  sulphuryl  chloride  when  brought  into  simul- 
taneous contact  with  sulphur  dioxide  and  chlorine1. 

In  these,  and  other  similar  changes,  one  of  the  necessary 
components  of  the  changing  system  apparently  remains  un- 
altered throughout  the  entire  reaction.  There  are  other 
chemical  changes  which^occur  only  in  presence  of  a  substance 
which  is  itself  unaltered  at  the  close  of  the  reaction,  but 
which  can  be  proved  to  undergo  a  cycle  of  changes,  through 
which  it  continuously  passes  and  repasses,  during  the  progress 
of  the  main  chemical  process.  Thus  the  presence  of  a  little 
aluminium  chloride  renders  possible  many  reactions  among 
carbon  compounds  which  do  not  proceed  in  the  absence  of 
this  substance ;  benzoic  acid,  for  instance,  is  produced  by 
passing  dry  carbonic  anhydride  into  hot  benzene  containing 
a  little  aluminium  chloride ;  and  benzene-sulphinic  acid  is 
produced  when  the  hydrocarbon  is  treated,  under  similar 
conditions,  with  sulphurous  anhydride.  Bleaching  powder  is 
wholly  decomposed,  yielding  calcium  chloride,  oxygen,  and 
water,  by  heating  with  a  relatively  very  small  quantity  of 
cobaltous  oxide.  It  has  been  shewn  that  the  aluminium 
chloride  in  one  case,  and  the  cobaltous  oxide  in  the  other,  is 
continuously  changed  and  reproduced  during  these  chemical 
actions. 

There  are  other  actions  which  appear  to  be  commenced 
by  the  presence  of  small  quantities  of  substances  which 
afterwards  take  no  part  in  the  action.  Thus  Wanklyn2  found 
that  dry  sodium,  even  when  fused,  does  not  combine  with 
dry  chlorine,  but  that  if  a  trace  of  moisture  is  present  the 
action  begins,  and  readily  continues.  Dixon3  has  also  shewn, 
that  a  mixture  of  perfectly  dry  carbon  monoxide  and  oxygen 

1  Schulze,  Journal  fur  prakt.  Chemie,  (2)  24.  168. 

2  Chem.  News,  20.  271,  3  Nature,  28.  551. 


376  CHEMICAL  KINETICS.  [§  179 

is  not  exploded  by  the  electric  spark,  but  that  the  ad- 
dition of  a  minute  quantity  of  water  causes  the  gases  to 
combine  quietly  when  submitted  to  the  action  of  the  elec- 
tric spark,  and  that  explosion  occurs  when  the  gases  are 
moist. 

Several  of  these  so-called  contact-actions  are  certainly  to 
be  placed  in  the  same  class  as  ordinary  chemical  changes,  and 
any  explanation  which  may  be  given  of  chemical  action  must 
include  these  as  special  cases.  Other  contact-actions,  e.g. 
those  of  spongy  platinum,  are  more  physical  than  chemical, 
and  in  so  far  as  this  is  so,  they  must  be  classed  with  those 
physical  phenomena  which  probably  form  part  of  every 
complete  cycle  of  chemical  change. 

The  remaining  instances  of  contact-actions  are  probably 
to  be  included  in  the  general  theory  of  the  influence  exerted 
by  changes  in  the  relative  masses  of  the  reacting  bodies  on 
the  course  of  chemical  reactions.  That  this  is  so,  in  some 
cases  at  least,  has  been  shewn  by  Ostwald,  in  his  study  of  the 
variation  produced  in  the  velocity  of  the  process  represented 
by  the  equation 

CH.COO.CH+HOH  =  CH 


by  the  presence  of  various  acids  which  take  no  direct  part 
in  the  chemical  reaction1. 

179.  Predisposing  affinity.  Such  a  chemical  change  as 
the  following  not  unfrequently  occurs.  If  the  compound 
AB  were  decomposed  by  the  body  C,  AC  and  B  would  be 
produced  ;  this  decomposition  does  not  however  take  place 
except  in  the  presence  of  a  third  body  D,  which  is  known  to 
form  a  compound  with  B,  viz.  BD.  The  initial  configuration 
of  the  system  is  represented  by  AB,  C,  D;  the  final  con- 
figuration by  A  C,  BD. 

The  substance  D  was  said  by  Berzelius  to  exert  a  pre- 
disposing affinity  on  B. 

Thus,  iodine  does  not  act  on  the  hydrocarbons,  as  a  group, 

1  Journal  fur  prakt.  Chemie,  (2)  28.  449.     This  paper  will  be  referred  to  in 
more  detail  in  chap.  in.  par.  224. 


§  179]  CHEMICAL  CHANGE. 

to  produce  iodo-derivatives,  but   these  derivatives  are 
duced  by  the  joint  action  of  iodine  and  iodic  acid, 

AB  +  C  =  no  action  ;  but  AB  +   C  +  Z>  =  AC  +  DB. 

(hydro-  (iodine)  (hydro-   (iodine)  (iodic        (ipdo-      (water  and 

carbon)  carbon)  acid)    derivative)     iodine) 

Again,  sulphur  dioxide,  oxygen,  and  water  very  slowly 
react  to  produce  sulphuric  acid,  but  if  these  three  substances 
are  brought  into  contact  with  sodium  chloride  at  about  400°, 
sodium  sulphate  is  rapidly  produced ;  the  sodium  chloride 
appears  to  act  upon  the  potentially  formed  sulphuric  acid 
with  production  of  sodium  sulphate  and  hydrochloric  acid. 

In  these  actions  it  is  probable,  or  indeed  almost  certain, 
that  the  reaction  AB-*rC=AC  +  B  does  occur  to  a  very 
small  extent  in  the  absence  of  the  third  body  D,  and  that 
the  subsequent  reaction  between  B  and  D  is  attended  with 
the  setting  free  of  a  considerable  quantity  of  energy  which  is 
used  in  doing  chemical  work  represented  by  the  primary 
change  AB  +  C=AC+B.  That  this  is  so  in  some  cases  is 
rendered  evident  by  Berthelot's  and  Ditte's  measurements 
of  the  quantities  of  heat  evolved  during  the  oxidation  of 
mercury  and  silver,  and  during  the  conversion  of  the  oxides 
so  formed  into  chlorides  and  iodides.  These  measurements 
shew  that  much  more  heat  is  evolved  during  the  latter,  than 
during  the  former  reactions  ;  thus, 

[Ag2O,  2KI]  -  [Ag2,  O]  =  29,800  gram-units  + . 

Now  silver  is  not  oxidised  by  dry  or  moist  oxygen,  but 
silver  oxide  is  rapidly  converted  into  iodide  by  immersion  in 
a  dilute  solution  of  potassium  iodide  ;  moreover  silver  is  itself 
easily  changed  into  silver  iodide  by  the  action  of  the  same 
solution ;  it  is  very  probable  that  in  the  last-named  change 
silver  oxide  is  produced  but  is  at  once  decomposed  with 
formation  of  silver  iodide  and  caustic  potash1. 

Another  instructive  instance  of  the  action  of  the  so-called 
predisposing  affinity  is  furnished  by  the  change  of  the  amides 
of  the  acetic  acid  series  into  ammonium  salts  of  the  same 
acids. 

1  Ditte,  Compt.  rend.  93.  415.    See  also  Berthelot,  Bull.  Soc.  chim.  (2)86.  487. 


37$  CHEMICAL  KINETICS.  [§  l8o 

The  change  RCONH2  +  HOH  =  RCOONH4  proceeds 
very  slowly;  but  if  an  acid,  e.g.  HC1,  H2SO4,  HNO3,  &c.  &c.  is 
added,  the  change  proceeds  rapidly,  each  acid  exerting  its 
own  specific  action  in  accelerating  the  process,  and  in  deter- 
mining the  limits  at  which  the  process  stops  for  given  con- 
ditions of  temperature  and  dilution.  As  we  shall  learn  here- 
after, the  action  of  the  acids  in  this  change  is  in  all  respects 
a  normal  one,  and  the  entire  process  belongs  to  the  ordinary 
type  of  chemical  change1. 

1 80.  Induction.  When  a  mixture  of  hydrogen  and  chlorine 
is  exposed  to  sunlight  hydrochloric  acid  is  rapidly  formed. 
Bunsen  and  Roscoe 2  noticed  that  when  a  mixture  of  these 
gases  in  equal  volumes  is  kept  for  some  time  in  the  dark,  and 
is  then  exposed  to  light,  an  appreciable  time  elapses  before 
any  chemical  action  begins,  and  that  the  velocity  of  the 
action  increases,  at  first  slowly,  then  more  rapidly,  until  a 
maximum  is  reached,  after  which  it  decreases.  If  the  reaction 
is  allowed  to  begin  and  the  mixture  is  then  placed  in  the 
dark,  the  process  stops,  and  on  again  bringing  the  mixed 
gases  into  sunlight  the  same  course  is  gone  through  as  before. 
The  greater  the  intensity  of  the  light  the  shorter  the  time 
which  elapses  before  the  maximum  action  is  reached.  If  a  very 
minute  trace  of  oxygen,  or  even  a  slight  excess  of  hydrogen, 
is  added  to  the  mixture  of  chlorine  and  hydrogen,  a  longer 
time  elapses  before  the  maximum  action  is  reached,  than  if 
a  mixture  of  the  pure  gases  in  equal  volumes  is  used  ;  indeed 
the  total  amount  of  action  seems  never  to  be  so  great  in  the 
former  as  in  the  latter  case.  Hence  a  minute  quantity  of 
oxygen  acts,  in  some  way,  in  decreasing  the  velocity  of  the 
change  H2  +  C12=2HC1. 

Bunsen  and  Roscoe  speak  of  the  mixture  of  hydrogen 
and  chlorine  as  exhibiting  a  resistance  to  chemical  change ; 
'  induction '  is  the  act  of  overcoming  this  resistance. 

Wright 3  noticed  the  occurrence  of  a  similar  phenomenon 
in  the  reduction  of  metallic  oxides  by  carbonic  oxide  and 

1  Seeposf,  chap.  in.  par.  222. 

2  Phil  Trans,  for  1857.  355. 

3  C.  S.  Journal  Trans,  for  1879.  475  ;  do.  for  1880.  757  (see  especially  p.  790). 


§:8o] 


CHEMICAL  CHANGE. 


379 


hydrogen.  An  appreciable  time  elapsed  before  any  action 
could  be  observed,  the  rate  of  action  then  slowly  increased, 
then  more  rapidly  increased  to  a  maximum,  after  which  it 
decreased.  A  curve  which  shall  represent  these  results 
will  have  (roughly)  this  general  form  (figure  i),  whereas  the 


FIG.  i. 


curve  representing  a  normal  process  of  dissociation  has  the 
general  form  shewn  in  figure  2. 


FIG.  i. 

The  phenomenon  was  more  marked,  in  Wright's  experi- 
ments, when  the  reduction  was  accomplished  by  means  of 
carbonic  oxide  than  when  hydrogen  was  the  reducing  agent ; 
the  changes  in  the  velocity  of  the  action  were  also  more 
noticeable  at  medium,  than  at  very  high  or  very  low  tem- 
peratures. 

It  is  not,  it  seems  to  me,  necessary  to  make  use  of  any 
special  term  indicative  of  a  difference  of  kind  between  these 
and  other  chemical  changes. 

Wright  has  shewn  that  the  observed  variations  of  the  rate 
of  the  reactions  are  largely  dependent  on  secondary  changes, 
and  on  the  physical  state  of  the  metallic  oxides  employed. 
These  reactions  are  but  fresh  illustrations  of  the  fact  we  so 
easily  forget  that  every  chemical  change  is  a  complex  occur- 
rence. The  formation  of  hydrochloric  acid  from  hydrogen 
and  chlorine  is  not  so  simple  as  the  equation  H2  +  C12 


CHEMICAL  KINETICS.  [§  l8O 

represents  it  to  be.  The  course  of  the  reaction  is  considerably 
modified  by  the  presence  of  minute  quantities  of  other  sub- 
stances, because  such  minute  quantities  further  complicate 
the  primary  change.  We  have  here  an  instance  of  the 
influence  of  secondary  forces  on  a  chemical  reaction.  Almost 
every  chemical  change  must,  it  would  appear,  consist  of 
several  parts,  one  of  which  may  be  regarded  as  primary  and 
the  others  as  secondary.  '  Induction '  therefore  becomes  an 
essential  feature  of  all  chemical  processes.  But  we  dp  not 
require  a  special  term.  Many  circumstances  may  occur  to 
prevent  the  attainment  by  a  changing  system  of  what  we  may 
call  its  normal  equilibrium.  But  this  condition  is  finally 
attained.  The  striving  towards  this  state  is  not  a  special 
feature  of  a  few  reactions,  but  is  an  essential  part  of  all 
reactions.  Small  alterations  of  the  conditions  under  which  a 
change  proceeds  may  much  retard  the  attainment  of  the  final 
equilibrium ;  e.g.  lowering  the  temperature  \  or  even  such 
mechanical  actions  as  greater  or  less  agitation,  or  removing 
part  of  the  changing  system  from  the  rest  of  the  system2. 

If  a  new  compound  is  introduced  into  the  changing  system 
the  rate  of  change  must,  we  should  think,  be  varied,  the  new 
substance  exerting  either  a  positive  or  a  negative  accelerating 
effect3;  but  if  the  normal  state  is  attained  in  the  long  run, 

1  Lowering  temperature  may  act  either  physically,  by  decreasing  the  molecular 
motions  and  hence  the  chances  of  decomposition  in  a  given  time,  or  chemically,  by 
bringing  about  the  formation  of  complex  molecular  groups.    An  example  of  both 
actions  has  been  worked  out  to  some  extent  by  the  author  (C.  S.  Journal  Trans, 
for  1880.  78.   See  also  Potilitzin  on  the  formation  of  hydrates  of  cobaltous  chloride ; 
Ber.  17.  276). 

2  When  one  or  more  of  the  constituents  of  a  chemical  system  is  gaseous,  altera- 
tions of  pressure  will  considerably  modify  the  direction  of  the  change  and  the 
final  configuration  of  the  system  ;  thus  a  solid  hydrate  CO2 .  .#H2O  may  be  formed 
by  compressing  CO2  and  H2O,  and  there  appears  to  be  a  definite  pressure  for  each 
temperature  at  which  the  hydrate  is  produced.     Probably  CO2  and  H2O,  CS2  and 
H2O,  N2O  and  H2O,  C2H2  and  H2O,  &c.,  form  a  series  of  hydrates  which  are 
decomposed  and  re-formed  according  to  changes  of  temperature  and  pressure : 
see  Dewar,  Proc.  R.  S.  30.  538;  Wroblewski,  Compt.  rend.  94.  212,  also  Wied. 
Ann.  17.  103 ;    Cailletet  and  Bordet,   Compt.  rend.  95.  58.      For   confirmatory 
evidence  of  a  more  directly  chemical  nature,  see  Ballo,  Ber.  15.  3003. 

3  See  Harcourt  and  Esson,  C.  S.  Journal,  20.  460.     This  paper  will  be  con- 
sidered in  section  2  of  this  chapter.     See  par.  196. 


§  l8l]  CHEMICAL  CHANGE.  381 

we  shall  have  the  phenomenon  called  by  Bunsen  and  Roscoe 
induction.  It  is  very  easy  to  overlook  parts  of  a  chemical 
change ;  one  is  apt  to  pay  attention  only  to  the  initial  and 
final  states  of  the  system.  Induction  may  thus  occur  and  not 
be  noticed  \ 

1 8 1.  Intfuence  of  mass.  If  it  is  admitted  that  the  course 
of  a  chemical  change  may  be  considerably  modified,  or  even 
completely  altered,  by  altering  the  conditions  under  which  the 
change  proceeds,  we  should,  I  think,  expect  to  find  that  vary- 
ing the  relative  masses  of  the  reacting  bodies  would  be  one  of 
the  commonest  ways  whereby  such  modification  or  alteration 
might  be  effected.  We  have  learned  what  importance 
Berthollet  attached  to  the  relations  between  the  masses  of 
substances  taking  part  in  a  chemical  process,  and  we  have 
seen  in  book  i.  that  attention  must  be  paid  to  these  relations 
in  discussing  the  data  of  thermal  chemistry,  even  when  the 
questions  under  consideration  rather  concern  the  composition 
than  the  actions  of  the  various  compounds. 

Recent  years  have  witnessed  the  publication  of  many 
important  researches  on  the  subject  of  mass-action ;  I  shall 
deal  with  Guldberg  and  Waage's  work  in  some  detail  here- 
after, at  present  I  wish  only  to  insist  on  the  importance  of 
considering  the  relative  masses  of  the  reacting  bodies  in  all 
processes  of  chemical  change,  and  to  remind  the  student  that 
this  factor  is  almost  universally  ignored  in  our  ordinary 
chemical  equations2. 

When  sodium  (or  potassium)  sulphate,  and  sulphuric  acid, 
are  allowed  to  react  in  equivalent  quantities  in  the  presence 
of  water,  the  relations  between  the  masses  of  Na2SO4, 
NaHSO4,  and  H2SO4,  found  in  the  solution  at  any  given 
temperature  are  conditioned  by  the  mass  of  the  water  pre- 
sent. There  is  probably  direct  mutual  action  between  the 
water  and  the  NaHSO4,  with  production  of  H2SO4  and 
Na2SO4,  the  reverse  change  being  brought  about  by  the 

1  The  chemical  changes  of  the  carbon  compounds  furnish  innumerable  instances 
of  the  importance  of  observing  the  intermediate  steps  in  these  changes. 

2  An  interesting  paper  on  this  subject  by  J.  Morris,  giving  references  to  all 
the  more  important  memoirs,  will  be  found  in  Annalen  213.  253. 


382  CHEMICAL  KINETICS.  [§  l8l 

H2SO4  which  has  been  added.  If  an  excess  of  Na2SO4  is 
added,  the  amount  of  water  being  large  and  remaining 
constant,  a  greater  quantity  of  NaHSO4  remains  unchanged 
to  Na2SO4  than  if  an  equivalent  excess  of  H2SO4  is  added. 
That  is  to  say,  the  action  of  Na2SO4  is  modified  by  the 
presence  of  the  water  in  a  way  different  from  that  in  which 
the  action  of  H2SO4  is  modified  ;  or,  to  put  this  statement  in 
another  form,  the  affinity  between  H2SO4  and  H2O  is  not  the 
same  as  the  affinity  between  Na2SO4  and  H^O1. 

Potilitzin's  investigations  of  the  influence  exerted  by 
variations  in  the  masses  of  the  acting  bodies  on  the  reactions 
which  occur  between  the  halogens  and  various  metallic  haloid 
salts  have  already  been  referred  to  (book  I.  chap.  IV.  par.  131). 
It  is  well  known  that  metallic  bromides  are  decomposed  by 
chlorine,  but  Potilitzin  has  shewn  that  the  reverse  change 
also  occurs  at  moderate  temperatures.  The  two  processes 
may  be  represented  thus, 


(i) 

(2)    *M.Cl+x'Br=x"MBr+x"C\  +  (x-x")  MCl  +  tf-x")  Br. 


Potilitzin's  results  teach  us  that  when  x  is  increased  in 
(2),  the  amount  of  MBr  formed  also  increases,  up  to  a 
certain  limit,  whereat  equilibrium  is  established.  The  same 
chemist  has  more  recently  examined  the  reactions  be- 
tween silver  chloride  (and  bromide),  and  metallic  bromides 
arid  iodides  in  aqueous  solutions  at  ordinary  tempera- 
tures2. 

The  various  changes  may  be  represented  thus, 


In  any  case  the  amount  of  action  is  dependent,  among 
other  conditions,  on  the  relative  masses  of  the  reacting  bodies. 
In  these,  as  in  his  earlier  experiments,  Potilitzin  finds  that  a 
condition  of  equilibrium  is  attained,  after  a  time,  by  the 

1  For  more  details  see  Ostwald,  Journal  fur  prakt.  Chemie  (2)  22.  305.     For 
older  investigations  of  the  modifying  influence  of  water  on  various  changes,  see 
H.  Rose,  Pogg.  Ann.  82.  545. 

2  See  abstract  in  Ber.  16.  3051. 


§  1 82]  CHEMICAL   CHANGE.  383 

distribution  of  the  halogens  between  the  silver  and  the  metal 
of  the  haloid  salt1. 

182.  From  what  has  been  said  in  the  preceding  para- 
graphs (178-181),  we  see  that  a  changing  chemical  system 
may  pass  through  a  series  of  stages  some  of  which  are  more 
stable  than  others.  It  may  indeed  be  that  certain  points  in 
the  series  are  so  unstable  that  they  are  not  marked  by  the 
production  of  what  we  are  accustomed  to  call  definite 
chemical  compounds2.  This  view,  of  well  marked  chemical 
compounds  being  the  most  stable  points  in  a  series  of 
potentially  existent  substances,  has  been  developed  by  Mills, 
starting  from  the  observations  of  Wurtz  on  the  polyethylenic 
glycols,  which  are  compounds  obtained  by  the  condensation 
of  n  molecules  of  ethylene  glycol  with  the  elimination  of 
n  —  i  molecules  of  water.  Mills  uses  the  expression  cumulative 
resolution*  to  mean  'the  combination  of  a  substance  or  mixture 
'of  substances  with  itself  n  times,  a  particular  portion  of  it 
'being  lost  each  time,  according  to  some  fixed  law.' 

The  general  equation  representing  a  process  of  cumulative 
resolution  is  given  by  Mills  in  this  form, 

nAJlpCy...  -(n-m)  AaBbCc  -••=An(a-a)+ma^-l>)+m&C(y-c)+mc  ', 

where  AaB^Cy  is  the  substance  which  undergoes  the  change, 
and  AaBbCc  is  that  portion  of  it  which  is  eliminated  at  each 
stage  of  the  process.  By  giving  values  to  n  varying  from 

1  For  a  fuller  discussion  of  the  influence  of  mass  on  chemical  changes  see  post, 
chap.  in.  section  1. 

2  It  should  be  noted  that  the  expressions  'stability,'  'stable  compound,'  and 
the  like,  are  somewhat  vague.     The  conditions  under  which  stability  is  predicated 
of  a  given  substance  must  be  stated  or  implied  if  the  word  is  to  convey  any  very 
definite  meaning.     Thus  zinc  methide  can  be  gasified  without  decomposition,  but 
when  this  compound  is  brought  into  contact  with  water  it  is  violently  decomposed, 
forming  zinc  hydrate  and  methane  ;  so  also  the  compound  K2O4  is  decomposed  at 
a  red  heat,  yielding  K2O  +  O3 ,  but  it  is  rapidly  acted  on  by  water  at  ordinary 
temperatures,  forming  KOH,  O2  and  H2O2.     The  fact  that  some  double  salts  are 
decomposed  in  aqueous  solutions  by  the  process  of  diffusion,  seems  to  illustrate 
the  position  that  certain  molecules,  or  molecular  groups,  which  shew  a  considerable 
range  of  what  may  perhaps  be  called  chemical  stability,  are  easily  broken  up  when 
small  alterations  are  made  in  the  physical  conditions  of  their  surroundings. 

3  See  Phil.  Mag.  (5)  3.  492  ;  or  the  article  '  Cumulative  resolution,'  in  the 
third  supplement  of  Watts's  Dictionary. 


384  CHEMICAL  KINETICS.  [§  183 

o  to  oo  various  formulae  are  obtained  for  the  cumulates,  or 
possible  products  of  the  change.  The  theory  may  be  applied 
to  the  action  of  water  on  bismuthic  nitrate,  whereby  a  series 
of  compounds  is  obtained,  each  less  nitrogenous  and  more 
bismuthic  than  the  preceding.  Thus, 

n  (Bi2O3 .  3N2O6)  -  (n  -  i)  N2O5=  Bi2nO3B .  N4n+2O10n+5  ; 

by  giving  various  values  to  n  from  o  to  oo  we  obtain  the 
formulae  of  all  possible  substances  between  Bi2O3.  3N2O5  and 
Bi2O3 .  2N2O5.  By  repeating  this  process  on  Bi2O3 .  2N2O5,  a 
series  of  possible  substances  is  obtained  of  which  the  limits 
are  marked  by  Bi2O3 .  2N2O5  and  Bi2O3 .  N2O5 ;  and  lastly  by 
a  repetition  of  the  process  of  cumulative  resolution  on  the 
last  compound,  a  third  series  is  obtained  ranging  from 
BiA-NAtoBip,1. 

183.  This  theory  points  to  the  frequent  existence  of  series 
of  substances  forming  connecting  links  between  those  com- 
paratively stable  compounds  which  can  be  separated  from 
the  materials  which  have  produced  them,  or  from  those  which 
are  the  products  of  their  decomposition. 

But  although  we  may  not  be  able  to  separate  and  obtain 
in  definite  form  the  comparatively  unstable  members  of  such 
series,  yet  it  may  be  possible  to  demonstrate  the  existence  of 
these  substances  by  indirect  methods. 

The  substances  in  question  exist  only  as  members  of  a 
system ;  apart  from  the  other  members,  or  from  some  of  the 
other  members,  they  undergo  decomposition. 

The  group  of  carbon  compounds  called  by  Armstrong 
and  Groves  Aldehydrols*  presents  us  with  examples  of  the 
phenomenon  now  under  consideration.  Aldehydrols  are 
almost  certainly  produced  in  the  first  stage  of  the  oxidation 
of  the  primary  ethylic  alcohols.  These  alcohols  are  oxidised 
only  in  presence  of  water ;  for  this  and  other  reasons  it  is 
very  probable  that  the  process  of  oxidation  is  represented 
by  the  equations 

1  For  other  applications  of  the  theory  see  the  article  in  Watts's  Diet. 

2  Organic  Chemistry,  1.  504. 


184]  CHEMICAL   CHANGE.  385 


(1)  CnH2)i  +  1C 

(2)  CHH2n  +  1CH(OH)2=CHH2B  + 

where  CnH2n+1  CH(OH)2  is  the  formula  of  an  aldehydrol1. 

Many  reactions  of  the  ethylic  aldehydes  are  explained  by 
assuming  the  existence  of  aldehydrols2  ;  the  properties  of 
chloral  hydrate  point  almost  with  certainty  to  the  formula 
CC13  .  CH(OH)2  for  this  compound3. 

The  aldehydrols  cannot  however  exist  except  as  members 
of  a  system  of  which  water  is  a  constituent  ;  the  system  is 
chemically  stable,  some  of  the  individual  members  when 
separated  from  the  others  are  very  unstable. 

Another  illustration  of  the  existence  of  a  compound  only 
in  the  presence  of  others  is  furnished  by  Traube's  preparation 
of  cupric  iodide  (CuI2)  in  aqueous  solution.  An  aqueous 
solution  of  this  compound,  the  supposed  non-existence  of 
which  has  been  often  noticed  as  peculiar,  can  be  prepared 
according  to  Traube  by  mixing  dilute  solutions  of  cupric  sul- 
phate and  potassium  iodide,  or  by  acting  on  cuprous  iodide 
(Cu2I2)  with  iodine  in  the  presence  of  a  large  quantity  of 
warm  water4. 

184.  Looking  back  on  the  conception  of  molecular  struc- 
ture which  was  reached  in  book  I.  (par.  64  et  seg.),  and  ap- 
plying to  it  the  further  knowledge  we  now  have,  we  should 
be  inclined  to  say  that  the  function  performed  by  a  given 
atom,  or  group  of  atoms,  in  this  molecule  or  in  that  cannot  be 
known  except  by  the  study  of  many  systems  wherein  the 
given  individual  occurs.  Before  we  have  a  knowledge  of  the 
chemical  properties  of  hydrogen,  for  instance,  we  must  study 
the  behaviour  of  this  element,  under  varying  conditions,  in 
its  compounds  with  metals,  with  nonmetals,  with  negative 
and  with  positive  groups  of  atoms,  &c.  It  might  indeed  be 
asserted  that  it  is  not  correct  to  say  that  the  molecule  of 

1  See  Armstrong  and  Groves,  loc.  cit.  1.  417  —  418. 

2  Ibid.  loc.  cit.  717  —  718.     See  also  p.  68  1  (formation  of  acetal  from  ethalde- 
hyde). 

3  Compare  the  properties  and  formation  of  chloral  hydrate  (ibid.  pp.  743  —  744) 
with  the  properties  of  chloral  alcoholate  (ibid.  p.  429). 

4  Ber.  17.  106-1. 

M.  C.  25 


386  CHEMICAL   KINETICS.  [§  185 

water  contains  hydrogen  or  oxygen,  just  as  it  is  not  correct 
to  say  that  the  molecule  of  sulphuric  acid  contains  the  atomic 
groups  SO3  or  H2O.  Mills1  goes  so  far  as  to  affirm  that 
water  is  not  represented  by  the  formula  H^O,  inasmuch  as  it 
is  a  homogeneous  substance  with  its  own  properties  ;  to  this 
we  might,  I  think,  reply  that  one  of  the  distinctive  properties 
of  water  is  implied  in  the  formula  H2O,  the  property  namely 
of  being  decomposable  into  H2  -f  O,  and  of  being  formed  by 
the  combination  of  H2  and  O. 

Every  chemical  substance  ought  to  be  regarded  in  its 
relations  to  other  substances ;  but  each  is  also  a  distinct  in- 
dividual. A  full  chemical  knowledge  of  any  substance  im- 
plies a  knowledge  of  all  the  possible  reactions  which  would 
occur  in  any  system  of  which  that  substance  may  form  a 
member.  The  whole  history  of  dualism  warns  us  against 
asserting  that  the  properties  of  any  chemical  substance  are 
independent  of  those  other  substances  with  which  it  is  or 
may  be  associated ;  but  at  the  same  time,  all  modern  research 
confirms  the  fundamental  conception  of  the  element  as  a 
distinct  form  of  matter  which  impresses  its  own  likeness  on 
all  the  compounds  of  which  it  forms  a  constituent. 


SECTION  II.     Chemical  Equilibrium. 

185.  Thus  we  come  back  to  the  conception  of  every 
chemically  stable  system  as  being  in  a  condition  of  equi- 
librium, which  is  the  result  of  the  actions  of  various  forces, 
some  of  which  are  what  we  usually  call  chemical,  and  others 
physical ;  if  one  of  these  forces  is  increased  the  equilibrium  is 
overthrown  and  the  system  undergoes  chemical  change. 

The  methods  used  in  attempts  to  solve  the  general  problem 
of  chemical  equilibrium  may  be  divided  into  two  classes,  (i) 
those  which  are  based  on  applications  of  the  molecular 
theory,  and  more  especially  on  the  kinetic  theory  of  gases ; 
(2)  those  which  are  essentially  thermodynamical. 

1  Phil.  Mag.  (5)  i.  i. 


§§  1 86,  187]  CHEMICAL  CHANGE.  387 

1 86.  Several  years  ago  Williamson1  put  forward  a  some- 
what vague  view,  to  the  effect  that  the  amount  of  chemical 
action    between   two   substances   may  be   measured   by  the 
relative  velocities  of  the  atomic  interchanges  taking  place  be- 
tween the  molecules  of  these  substances. 

Arguing  from  the  reactions  of  substitution  among  carbon 
compounds,  especially  the  substitution  of  H  in  H2SO4  by 
CnH2B+1  groups  and  vice  versa,  Williamson  concluded,  that  if 
chemically  similar  atoms  continually  change  places  in  reacting 
molecules,  much  more  likely  is  it  that  chemically  identical 
atoms  will  undergo  intermolecular  change.  'We  are  thus 
'forced  to  admit  that  in  an  aggregate  of  molecules  of  any 
'compound  there  is  an  exchange  continually  going  on  be- 
'  tween  the  elements  which  are  contained  in  it.'  In  a  drop  of 
an  aqueous  solution  of  hydrochloric  acid,  for  instance,  '  each 
'  atom  of  hydrogen  is  constantly  changing  places  with  other 
'atoms  of  hydrogen';  when  a  solution  of  copper  sulphate  is 
added  to  hydrochloric  acid,  then  the  interchange  of  copper 
for  copper,  and  of  hydrogen  for  hydrogen,  proceeds  as  before, 
but  in  addition  to  this  '  the  hydrogen  does  not  merely  move 
'  from  one  atom  of  chlorine  to  another,  but  in  its  turn  also 
'  replaces  an  atom  of  copper,  forming  chloride  of  copper  and 
'sulphuric  acid.'  When  one  product  is  insoluble  it  is  re- 
moved, and  so  almost  the  whole  of  one  of  the  original  sub- 
stances is  decomposed. 

187.  Pfaundler2  has  developed  a   hypothesis   somewhat 
similar   to   that   put    forward    by   Williamson.      Pfaundler's 
hypothesis  is  indeed  grounded  on  the  second  law  of  thermo- 
dynamics, but  its  development  proceeds  on  the  lines  of  the 
molecular  theory. 

Let  there  be  two  gases,  AB  and  CD,  formed  from  A,  B,  C 
and  D,  with  the  evolution  of  less  heat  than  that  which  ac- 
companies the  formation,  from  the  same  constituents,  of  two 
other  gases,  AD  and  BC\  then  the  change  from  AD,  BC 
back  to  AB,  CD  will  necessarily  be  attended  with  absorption 

1  C.  S.  Journal,  4.  no — 112.     (See  also  do.  4.  229;  also  Phil.  Mag.  (3)  37. 
350-) 

-  Ann.  Jubelbd.  182  :  and  do.  131.  55  et  seq.  (especially  pp.  66 — 71). 

25—2 


388  CHEMICAL  KINETICS.  [§  1  87 

of  heat.  In  other  words  the  reverse  operation,  thermally  con- 
sidered, will  be  a  negative  change,  and  it  must  be  accom- 
panied by  a  compensating  positive  change. 

Let  heat  pass  from  a  hotter  body  to  the  mixture  of  AD 
and  BC  molecules,  then  this  addition  of  heat  (i.e.  this  positive 
change)  may  be  accompanied  by  an  equivalent,  or  less  than 
an  equivalent,  negative  change  ;  the  re-formation  of  AB  and 
CD,  or  generally  an  action  involving  absorption  of  heat, 
may  occur. 

Suppose  that  in  a  given  space  there  is  a  limited  number 
of  molecules  AB,  CD,  AD,  and  BC,  that  no  heat  enters  or 
leaves  the  system,  and  that  the  temperature  of  the  space 
remains  constant  ;  then  a  series  of  molecules  may  be  pro- 
duced, represented  by  the  formulae  AC,  BD,  A  A,  BB,  CC, 
nri  (AC  (AA  (AA  (BB  (  BB  . 
2)1)9  \3D>\B2>\CC>\CO'\  DD>  &c"  But  accordinS  to 
the  hypothesis  already  made,  the  production  of  A  A,  BB...DD, 
must  be  accompanied  by  an  absorption  of  heat.  The  formation 
of  the  elementary  molecules,  A  A,  &c.  would  require  the 
greatest  absorption  of  heat  ;  on  the  other  hand,  the  formation 

(  AB 
of  the  complex  molecules  \  rn,  &c.  will,  as  a  rule,  be  attended 

I 


with  evolution  of  heat.  If  molecules  are  formed  with  heat- 
absorption,  such  changes  must  be  accompanied  by  others 
wherein  equivalent  quantities  of  heat  are  evolved. 

Pfaundler  then  gives  a  rough  classification  of  these  positive 
and  negative  thermal  changes1. 

The  relations  between  the  distribution  of  the  energy  and 
the  distribution  of  the  molecular  configurations  in  such  a 
system  are  considered  in  Pfaundler's  second  paper. 

The  hypothesis  asserts  that  exchange  of  atoms,  or  atomic 
groups,  is  constantly  proceeding  in  chemical  systems;  but 
the  consideration  of  this  withdrawal  and  replacement  of 
atoms,  from  and  in  the  molecules  of  the  reacting  substances, 
can  be  approached  only  by  statistical  methods.  There  may 
be  more  withdrawals  than  replacements  of  individual  atoms, 

1  See  />*££•.  Ann.  Jubelbd.  187—8. 


§  l8/]  CHEMICAL   CHANGE.  389 

but,  when  equilibrium  is  established,  the  mean  number  of 
each  in  a  given  time  is  equal. 

But  why  do  exchanges  of  parts  of  molecules  occur  ? 
Pfaundler's  hypothesis  refers  these  atomic  exchanges  to 
momentary  differences  in  the  states  of  motion  of  individual 
molecules,  which  is  a  fundamental  point  in  the  kinetic  theory 
of  gases. 

Consider  the  motion  of  agitation  of  the  molecules,  and 
the  motion  of  the  parts  of  the  molecules ;  the  kinetic  theory 
asserts  that,  at  a  constant  temperature,  the  sum  of  the  kinetic 
energies  of  these  two  motions  is  constant,  and  also  the  sum 
of  each  is  constant,  but  th^  two  motions  may  be  very 
differently  distributed  among  the  individual  molecules. 
Calling  the  energy  of  agitation  of  the  molecules  of  a  system 
(a),  and  the  energy  of  rotation  of  the  parts  of  the  molecules 
(b\  there  are  four  limiting  cases  for  the  distribution  of  these 
two  energies. 

Case  i  :  (a)  and  (b)  are  both  at  a  maximum ; 
„     2  :  (a)  and  (b)  are  both  at  a  minimum  ; 
„     3  :  (a)  is  at  a  minimum,  and  (b)  at  a  maximum  ; 
„     4 :  (a)  is  at  a  maximum,  and  (b)  at  a  minimum. 

Pfaundler  illustrates  these  four  cases  as  follows : 

(1)  Two  molecules,  AB  and  CD,  collide,  so  that  at  the 
next  instant  (a)  is  wholly  or  almost  wholly  changed  to  (b) ; 
therefore  (b)  is  greater  than  the  maximum  for  stability  in 
both  molecules.     The  molecules  AB  and  CD  separate  into 
A,  B,  C,  and  D. 

(2)  Two  molecules,  AB  and  CD,  collide ;  it  is  possible 
that    the    resulting    internal    motion    of    the    parts   of    the 
molecules  is  too  small  to  separate  AB  and   CD  into  their 
constituents ;  but  is  also  too  small  to  prevent  the  formation 
of  the  complex  molecule  A  BCD,  which  is  therefore  produced. 

(3)  After  collision  the  resulting  internal  motion  is  too 
small  to  separate  AB  and  CD  into  their  constituent  parts, 
but  is  sufficient  to   prevent   the   formation   of  A  BCD;    the 
original    molecules,    AB    and    CD,    therefore    rebound    un- 
changed. 


390  .        CHEMICAL  KINETICS.  [§  l8/ 

(4)  The  complex  molecule  A  BCD  is  momentarily  formed  ; 
but  the  blow  of  AB  on  CD  being,  according  to  the  simplest 
hypothesis,  direct  and  central,  the  whole  system  vibrates. 
Whether  A  BCD  shall  separate  into  AB  and  CD,  or  into  AC 
and  BD,  depends  on  the  magnitude  of  the  affinities  of 
A,  B,  C,  and  D  for  each  other,  and  also  on  the  previous 
internal  motions  of  the  parts  of  AB  and  CD ;  the  greater 
this  internal  motion,  the  more  readily  will  the  change  now 
proceed  in  the  direction  of  AC  and  BD,  because  the  further 
will  the  separation  of  A  from  By  and  of  C  from  D,  have 
been  already  carried. 

Hence,  Pfaundler  concludes,  the  nature  (Art)  of  a  decom- 
position depends  on  the  mutual  affinities  of  the  constituents 
of  the  system,  and  also  on  the  conditions  of  motion  of  these 
constituents  ;  reactions  may  occur  in  directions  apparently 
opposed  to  the  affinities. 

Cases  (3)  and  (4)  will  probably  occur  more  frequently 
than  cases  (i)  and  (2),  because  the  former  require  smaller 
differences  between  the  motions  of  the  individual  molecules 
than  the  latter. 

Remembering  that  the  kinetic  energy  of  the  atoms  in  the 
various  molecules  may  be  associated  with  many  kinds  of 
motion  (swinging  motions,  rotations,  &c.),  one  recognises 
how  manifold  may  be  the  possible  distributions  of  molecular 
configuration.  The  molecules  may  undergo  many  changes 
(the  mean  temperature  of  the  system  remaining  constant) 
which  we  should  regard  as  departures  from  a  normal  con- 
dition obtaining  if  all  the  molecules  were  simultaneously  in 
the  same  state.  The  simplest  of  such  departures  from  the 
average  state  is  exhibited  by  the  processes  of  dissociation, 
which  is  however  only  a  special  (although  the  simplest)  case 
of  '  simultaneous  reciprocal  reactions  in  consequence  of  varia- 
'tions  in  the  motions  of  individual  molecules1.' 

1  Pfaundler  devotes  some  space  to  considering  the  best  name  to  give  to  the 
general  phenomenon  of  which  he  says  dissociation  is  a  special  case ;  he  finally 
adopts  the  expression  '  competition  (concurrenz)  of  the  molecules '  (see  Pogg.  Ann. 
Jubelbd.  189).  This  theory  of  chemical  change  developed  by  Pfaundler  is  not 
opposed  to  the  results  of  recent  electrical  investigations  regarding  chemical  affinity ; 
,  chap.  ill.  par.  252. 


§§  1 88,  189]  CHEMICAL  CHANGE.  39! 

1 88.  The  hypothesis  of  Pfaundler   indicates  that  there 
must  be  a  temperature  at  which  any  given  chemical  change 
begins,  and  that  for  every  temperature  there  is  a  limit  beyond 
which    the    change    does    not    proceed.      Only   a    few   de- 
terminations  have  as  yet  been   made  of  the  limiting   con- 
ditions of  chemical  operations,  and  of  the  rates  at  which  the 
operations  proceed  within  these  limits. 

Menschutkin's  experiments  on  the  rates  and  limits  of 
etherification1,  which  have  been  partly  considered  in  book  I., 
and  more  especially  Ostwald's  studies  of  the  velocities  of 
various  chemical  changes2,  furnish  examples  of  the  kind  of 
work  that  is  required3.  [For  a  few  examples  of  such  investi- 
gations see  post,  pars.  195 — 199.] 

189.  Pfaundler's     treatment    of    chemical    equilibrium 
throws  some  light  on  the  questions  of  nascent  actions  dis- 
cussed from  the  statical  point  of  view  in  book  I.  (chap.  II. 
section  i).     These  actions  may  I  think  be  treated  as  special 
instances  of  equilibrium  coming   under  Pfaundler's  case  (4) 
[see  ante,  p.  389].     If  we  grant  that  when  hydrogen,  for  in- 
stance, is   evolved  by  the  action  of  zinc  on  dilute  sulphuric 
acid,  the  gas  consists  for  a  short  but  appreciable  time  for  the 
most  part  of  atoms  (or  monatomic  molecules),  then  we  have  a 
system  wherein  the  motion  of  rotation  of  the  parts  of  one 
kind  of  the  molecules  A  A  (or  BE)  is  so  great  that  most  of 
these  molecules  are  actually  separated  into  their  constituent 
parts  A,  A  (or  B,  B) ;  hence,  if  there  be  within  the  sphere  of 
action  another  set  of  molecules,  CD,  the  change  will  proceed  in 
the  direction  indicated  by  the  formation  of  the  new  molecules 
AC  and  AD.     If  however  the  energy  due  to  the  separation 


1  See  ante,  book  I.  chap.  IV.  pars.  157 — 8;  a\sv  post,  par.  197. 

2  See  post,  chap.  in.  par.  222. 

3  Hood's  experiments  (Phil.  Mag.  (5)  6.  371)   on  the  oxidation  of  ferrous 
sulphate  solution  by  potassium  chlorate  led  to  the  probable  conclusion  that  the 
amount  of  chemical  change  varied  as  the  square  of  the  temperature.     Warder 
(Amer.  Chem.  Journal,  3.  No.  5)  has  arrived  at  the  same  conclusion  from  his  study 
of  the  influence  of  temperature,  &c.,  on  the  rate  of  saponification  of  ethylic  acetate. 
Mills  and  Mackey  (Phil.  Mag.  (5)  16.  429)  have  examined  the  relations  between 
the  strength  of  aqueous  sulphuric  acid  and  the  line  of  '  no  chemical  change ',  for 
given  temperatures,  in  the  reaction  between  that  acid  and  metallic  zinc. 


3Q2  CHEMICAL   KINETICS.  [§  190 

of  A  A  into  A  and  A  is  not  employed  in  bringing  about  the 
secondary  change,  namely,  formation  of  AC  and  AD,  then  the 
separated  atoms  swing  back  into  their  previous  configuration, 
and  the  whole  system  assumes  a  new  condition  of  equi- 
librium. 

Moreover,  whether  the  molecules  AA  (or  BB)  shall,  or 
shall  not,  be  separated  into  the  atoms  A,  A  (or  B,  B)  must  to 
a  great  extent  depend  on  the  materials  from  which,  and  the 
conditions  under  which,  these  molecules  have  been  produced. 
Again,  whether  these  monatomic  molecules  (A}  A),  having 
been  produced  shall  react  with  the  molecules  CD,  to  form  A  C 
and  AD,  or  shall  swing  back  to  the  configuration  AA,  must 
be  conditioned,  among  other  things,  by  the  nature  of  the 
molecules  CD.  Finally  the  equilibrium  of  the  entire  system 
will  vary  with  variations  in  the  rate  of  production  of  A,  A, 
and  with  variations  of  physical  conditions,  among  which  con- 
ditions temperature  will  be  especially  important. 

190.  Pfaundler  shews  that  his  hypothesis  affords  a  fairly 
satisfactory  explanation  of  many  cases  of  contact-action  and 
predisposing  affinity^,  this  explanation  being  based  on  the 
deduction  from  the  hypothesis  in  question,  that  the  number 
of  molecules  of  one  kind  present  at  any  time  in  a  changing 
system  must  depend  on  the  nature  and  number  of  all  the 
molecules,  of  whatever  kind,  which  comprise  the  system. 

Thus  let  a  gaseous  system  consist  of  the  molecules  AB, 
BC,  A,  and  C.  Let  the  temperature  be  constant,  but  let  the 
mass  of  AB  be  increased ;  the  number  of  free  molecules  of  C 
decreases,  more  of  BC  forms,  but  at  the  same  time  more 
molecules  of  BC  are  decomposed  in  a  given  time  than  before 
the  number  of  AB  molecules  was  increased. 

Decreasing  the  amount  of  A  will  decrease  the  decompo- 
sition of  BC  by  A,  and  hence  will  decrease  the  number  of 
C  molecules.  If  AB  increases,  and  A  simultaneously  de- 
creases, C  will  soon  disappear.  On  the  other  hand  it  is 
evident  that  if  AB  decreases,  and  A  increases,  the  number  of 
molecules  of  C  will  also  increase2. 

1  See  ante,  pars.  178,  179. 

2  See  also  Hicks,  Phil.  Mag.  (5)  4.  82. 


§§  191,  IQ2]  CHEMICAL  CHANGE.  393 

191.  Dissociation  appears  as  a  particular  instance  of  the 
application  of  Pfaundler's  hypothesis  of  chemical  equilibrium1. 
This  subject  has  been  treated  by  more  purely  mathematical 
methods  by  Hicks2,  who  has  arrived  at  results  very  similar  to 
those  obtained  by  Pfaundler.     Hicks  has,  it  is  true,  failed  to 
deduce  any  simple  relation  between  the  mutual  atomic  actions 
of  an  elementary  gas  and  the  phenomena  which  attend  the 
dissociation  of  the  molecules  of  that  gas,  but  he  arrives  at  the 
same  general  conception  of  a  gaseous  system  as  Pfaundler 
had  done  before,  the  conception,  namely,  of  equilibrium,  even 
the  equilibrium  of  an  elementary  gas,  as  the  result  of  the 
continual  interchange  of  atoms,  or  atomic  groups,  between 
the  molecules  of  the  constituents.    Hicks  also  points  out  that  it 
may  be  possible  to  treat  mathematically  the  questions  pre- 
sented by  the  phenomenon  of  the  passage  of  the  same  gaseous 
system  through  various   states,  or  phases,  of  chemical  and 
physical    equilibrium,  one   of  which   phases   is  always   con- 
siderably more  stable,  as   regards   temperature  at  any  rate, 
than  the  others. 

192.  In  1873  Horstmann3  propounded  a  thermodynamical 
theory  of  dissociation  which  is  also  applicable,  in  its  broad 
features,  to  other  cases  of  chemical  equilibrium.     The  funda- 
mental position  of  Horstmann's  theory  is  that  the  degree  of 
dissociation  of  any  system  is  conditioned  by  all  the  circum- 
stances which  determine  the  value  of  the  entropy  of  that 
system.     The   system    attains   stable   equilibrium    when   the 
entropy  is  as  great  as  possible  under  the  conditions.     To  de- 
termine  the   conditions   under   which   the    entropy    of    any 
dissociating  system  is  at  its  maximum  is  therefore,  according 
to  Horstmann,  to  solve  the  problem  of  dissociation.     The 

1  I  have  devoted  considerable  space  to  an  account  of  Pfaundler's  papers,  because 
they  contain,  so  far  as  I  know,  the  only  attempt  that  has  been  made  to  develope  a 
kinetical  hypothesis  of  chemical  action  in  terms  of  the  molecular  theory  of  gases. 
It  is  however  questionable  whether  hypotheses  such  as  this  are  of  much  scientific 
value.     We  have  no  exact  knowledge  of  the  forces  acting  between  the  parts  of 
molecules ;  and  we  know  almost  nothing  of  the  mechanism  whereby  the  energy 
absorbed  by  this  or  that  substance  is  employed. 

2  Phil.  Mag.  (5)  4.  80  and  1 74. 

3  Annalen  170.  192. 


394  CHEMICAL  KINETICS.  [§  193 

maximum  entropy  is  attained  when  as  many  molecules  as 
possible  are  decomposed  with  the  minimum  consumption  of 
heat,  and  when  the  molecules  of  all  the  gases  forming  the 
system  are  as  far  as  possible  separated  from  one  another,  (i.  e. 
when  the  disgregation  [see  chap.  III.  par.  239]  of  the  system 
is  at  a  maximum).  But  these  conditions  are  fulfilled  before 
complete  decomposition  occurs,  therefore  only  a  portion  of 
the  original  substance  is  separated  into  its  constituents1. 

193.  But  the  whole  subject  of  chemical  equilibrium  has 
been  treated  in  a  masterly  manner  by  Willard  Gibbs2. 

The  fundamental  principle  on  which  the  theory  of  Gibbs 
is  founded  is,  that,  when  the  entropy  of  any  isolated  material 
system  has  reached  a  maximum,  the  system  will  be  in  a  state 
of  equilibrium.  The  form  in  which  Gibbs  puts  this  state- 
ment is  as  follows : 

'  For  the  equilibrium  of  any  isolated  system  it  is  necessary 
*  and  sufficient  that  in  all  possible  variations  of  the  state  of 
'  the  system  which  do  not  alter  its  entropy,  the  variation  of 
1  its  energy  shall  either  vanish  or  be  positive.' 

The  stability  of  a  system  depends  upon  the  '  magnitudes ' 
of  the  system,  which  are 

(1)  the  component  masses  of  its  constituents,  ml  ...  mnt 

(2)  the  volumes  „  „  vl  ...vn  , 

(3)  the  entropy  „  „  fa  ...  <£„; 

and  upon  the  '  intensities '  of  the  system,  which  are 

(4)  the  pressure/, 

(5)  the  temperature  /  (reckoned  on  the  absolute  or  thermodynamic  scale), 

(6)  the  potentials  of  the  components  /^  ...  /*«. 

The  potential  of  a  component  is  thus  defined  by  Gibbs: 

'  If  to  any  homogeneous  mass  in  a  state  of  hydrostatic 

'  stress  we  suppose  an  infinitesimal  quantity  of  any  substance 

'to   be   added,  the    mass   remaining  homogeneous,   and   its 

'  entropy  and  volume  remaining  unchanged,  the  increase  of 

1  Horstmann's  treatment  of  this  subject  is  not,  I  think,  very  happy.     The 
thermodynamical  conception  of  entropy  can  scarcely  be  applied  to  statistical  ques- 
tions regarding  the  motions  of  molecules. 

2  Amer.  Journ.  of  Sci.  and  Arts  (3)  16.  441  :  18.  277.   See  also  Clerk  Maxwell, 
South  Kensington  Science  Conferences,  [1876]. 


§  193]  CHEMICAL   CHANGE.  395 

'  the  energy  of  the  mass  divided  by  the  quantity  of  the  sub- 
'  stance  added  is  the  potential  for  that  substance  in  the  mass 
*  considered.' 

Clerk  Maxwell  defines  the  potential  for  any  substance  as 
'the  intensity  with  which  the  system  tends  to  expel  that 
'  component  from  its  mass.' 

The  '  entropy  of  a  body  is  a  quantity  such  that  without  a 
change  in  its  value  no  heat  can  enter  or  leave  the  body';  as 
the  isothermal  lines  of  a  gas  furnish  a  scale  of  temperature,  so 
the  adiabatics  furnish  a  scale  of  entropy  \ 

Gibbs  then  attempts  to  determine  the  relations  between  the 
energy  of  homogeneous  masses  and  the  variables  mv  m^...mn, 
v,  </>,/,  ty  fjbv  fjLz.../jLn.  Many  different  homogeneous  bodies  can 
be  formed  out  of  any  set  of  component  substances  ;  any  such 
body  considered  solely  with  regard  to  its  composition  and 
thermodynamic  state  is  called  by  Gibbs  a  phase  of  the  system 
considered.  Two  or  more  phases  may  coexist.  If  the  sta- 
bility of  phase  A  is  positive  with  regard  to  that  of  another 
phase,  B,  then  phase  A  is  stable ;  but  if  the  stability  of  A  is 
negative  with  regard  to  B,  then  phase  A  will  tend  to  pass  into 
phase  B.  Phase  A  may  be  stable  in  itself  but  may  have  its 
'  stability  destroyed  by  contact  with  the  smallest  portion  of 
'  matter  in  certain  other  phases';  certain  changes  may  therefore 
be  commenced  by  very  small  exciting  causes 2.  The  possible 
existence  of  unstable  phases  in  heterogeneous  systems  has 
of  course  been  known  to  chemists,  although  such  phases  have 
been  almost  entirely  overlooked  in  chemical  investigations ; 
but  we  are  taught  by  the  researches  of  Gibbs  that  the  con- 
ditions of  existence  of  such  phases,  and  their  relations  to 
stable  phases  of  the  same  systems,  can  be  deduced  from  the 
principles  of  the  conservation  and  degradation  of  energy. 

Gibbs  then  proceeds  to  find  the  *  fundamental  equations ' 
for  ideal  gases  and  mixtures  of  gases  ;  a  fundamental  equa- 
tion being  one  between  the  energy,  entropy,  volume,  and 
component  masses  of  a  system ;  '  all  the  thermal,  mechanical 

1  See  on  this  subject  Clerk  Maxwell's  Heat,  p.  161 :  also  192 — 194  (6th  ed.). 

2  For  a  fuller  treatment  of  the  'criterion  of  stability'  of  homogeneous  fluids, 
see  Gibbs's  first  paper  (loc.  cil.),  p.  447. 


396  CHEMICAL   KINETICS.  [§  193 

and  chemical  properties  of  a  compound,  so  far  as  active 
tendencies  are  concerned  [depend  on  these  relations],  when  the 
form  of  the  mass  does  not  require  consideration.' 

When  the  energy  of  a  mixture  of  gases,  some  of  the  proxi- 
mate components  of  which  can  be  formed  out  of  others,  has 
the  least  value  consistent  with  its  entropy  and  volume,  we 
have  what  is  called  by  Gibbs  'a  phase  of  dissipated  energy'; 
for  such  a  phase  the  potentials  for  the  proximate  components 
must  '  satisfy  an  equation  similar  to  that  which  expresses  the 
relation  between  the  units  of  weight  of  these  components'. 
Thus  if  the  components  of  the  system  are  hydrogen,  oxygen, 
and  water-gas,  the  potentials  for  these  substances  must  satisfy 
the  relation 


inasmuch  as  8  of  oxygen  +  I  of  hydrogen  =  9  of  water. 

Dissociable  gases  are  called  by  Gibbs  '  gas-mixtures  with 
convertible  components  '.  If  the  general  laws  of  ideal  gas- 
mixtures  apply  to  these  gases,  it  may  be  shewn  that  the 
phases  of  dissipated  energy  are  the  only  phases  that  can 
exist.  An  equation  may  be  obtained  for  the  relations  of 
pressure,  temperature,  and  density  in  such  a  mixture,  and  the 
results  calculated  by  means  of  this  equation  may  be  compared 
with  experimentally  determined  numbers.  If  the  calculated 
agree  with  the  experimentally  determined  results,  then  some 
of  the  general  laws  of  chemical  equilibrium  'may  be  deduced 
from  the  study  of  ideal  gas-mixtures. 

Take  for  instance  the  dissociation  of  N2O4  ;  equilibrium  is 
established  at  a  given  temperature  for  the  system  consisting 
of  N2O4  and  NO2.  The  assumption  made  by  Gibbs  for  this 
system  is,  that  equilibrium  is  determined  by  the  condition 
that  its  entropy  has  the  greatest  possible  value  consistent 
with  the  energy  and  the  volume  of  the  system  ;  he  thus 
obtains  an  equation  between  m^,  m^...mn,  t>  and  vl. 

Gibbs  compares  the  observed  densities  of  the  vapours  of 
nitrogen  peroxide,  formic  acid,  acetic  acid,  and  phosphorus 

1  For  the  development  of  the  formula  in  question  into  a  form  which  admits  of 
ready  application  to  such  cases  as  the  dissociation  of  N2O4,  see  Gibbs's  second 
paper,  loc.  cit.,  pp.  280  —  281. 


§  193]  CHEMICAL  CHANGE.  397 

pentachloride  at  different  temperatures  and  pressures  with  the 
densities  calculated  by  his  formula.  The  agreement  is  on 
the  whole  very  satisfactory,  although  there  are  some  dis- 
crepancies, especially  in  the  case  of  phosphorus  pentachloride. 

As  an  example  of  a  system  existing  under  special  con- 
ditions in  a  phase  beyond  the  limits  of  absolute  stability,  and 
of  the  sudden  overthrow  of  the  equilibrium  of  such  a  system 
by  small  exciting  causes,  Clerk  Maxwell  (South  Kensington 
Sci.  Conferences,  1876)  notices  the  case  of  water,  freed  from 
air,  remaining  in  the  liquid  state  at  a  temperature  much  above 
the  boiling  point  normally  corresponding  to  the  existent 
pressure,  but  exploding  instantly  it  comes  in  contact  with 
any  gas.  He  also  cites  the  equilibrium  of  a  37  per  cent, 
aqueous  solution  of  calcium  chloride  cooled  below  37°,  as 
described  by  Guthrie  in  his  study  of  cryohydrates. 

Many  of  the  examples  already  given  of  contact-actions 
and  predisposing  affinity  (pars.  178,  179)  may  serve  to 
illustrate  the  influence  exerted  by  matter  in  one  phase 
when  brought  into  contact  with  material  systems  in  other 
phases.  If  the  latter  systems  are  in  indifferent  equilibrium,  a 
very  small  external  action  may  suffice  to  produce  a  large 
result,  because  when  the  equilibrium  has  been  overthrown 
the  components  of  the  system  are  free  to  act  and  react,  and  a 
considerable  chemical  change  may  occur. 

It  may  be  possible  to  convert  a  phase  of  absolute  stability 
first  into  one  of  relative  instability,  and  then  into  one  of 
absolute  instability,  by  contact  with  matter  in  another  phase, 
i.e.  in  ordinary  chemical  language  by  the  action  of  a 
reagent1. 

If  the  kinetic  theory  of  chemical  action  developed  by 
Pfaundler  and  others  is  in  the  main  accepted,  then  it  would 
appear  that  many,  if  not  indeed  most,  chemically  heterogeneous 
systems,  the  average  state  of  which  remains  constant  (i.e.  sys- 

1  A  mixture  of  marsh  gas  and  oxygen  which  undergoes  slow  combustion  at  a 
certain  temperature  will  explode,  according  to  Mallard  and  Le  Chatelier,  after 
the  expiration  of  a  variable  time  which  is  longer  the  lower  the  temperature  [see 
Compt.  rend.  91.  825],  We  have  here  probably  an  example  of  the  passage  from 
a  stable  phase,  through  a  relatively  unstable,  to  an  absolutely  unstable  phase. 


CHEMICAL   KINETICS.  [§§  1 94,  195 

terns  which  are  not  undergoing  what  is  usually  called  chemi- 
cal change)  are  really  in  some  one  of  those  phases  of  relative 
instability  which  are  easily  overthrown  by  contact  with  small 
quantities  of  matter  in  other  phases.  The  more  complex  the 
possible  actions  and  reactions  between  the  components  of  any 
chemically  heterogeneous  system,  the  more  probable  will  be 
the  occurrence  of  relatively  unstable  phases,  and  the  more 
easily  will  what  may  be  called  the  normal  course  of  the 
chemical  change  be  turned  aside  by  small  changes  in  the 
magnitudes  or  intensities  of  the  system.  '  Chemical  induction ' 
will  be  a  marked  feature  of  such  processes  \ 

Molecular  compounds  may  be  regarded  as  systems  in 
phases  of  indifferent  equilibrium 2. 

194.  The  considerations  regarding  chemical  equilibrium 
which  have  been  sketched  in  the  preceding  paragraphs  shew 
the  great  importance  of  accurate  determinations  of  the  course 
and  rate  of  chemical  changes.     A  considerable  amount  of 
work  has  been  done  in  this  direction,  but  much  more  regular 
and  systematised  research  is  needed  before  many  generalisa- 
tions can  be  made. 

195.  In    1855,   Gladstone   studied   various   reactions   in 
which  ferric  salts  reacted  with  potassium  sulphocyanide,  &c. 
in  aqueous  solutions,  with  the  production  of  reddish  coloured 
compounds.    The  amount  of  change  was  determined  by  mea- 
surements of  the  depth  of  colour  produced 3. 

Gladstone  concluded  from  his  experiments  that  in  chemical 
operations  wherein  all  the  reacting  bodies  and  all  the  possible 
products  are  in  solution,  the  rate  of  change  depends  on  the 
rate  of  mutual  diffusion  of  the  various  substances,  and  the 
'  coefficients  of  affinity '  of  the  reacting  bodies. 

1  When  we  have  more  data  regarding  the  differences  between  the  quantities  of 
energy  associated  with  different  isomerides,  it  is  possible  that  the  whole  theory  of 
isomerism,  regarded  from  the  thermodynamical  point  of  view,  may  be  developed 
from  the  fundamental  principle  of  equilibrium  as  laid  down  by  Gibbs. 

2  See  especially  Graham's  work  on  the  colloidal  and  crystalloidal  states  of 
matter,  more  particularly  his  paper  in  Phil.  Trans,  for  1861.  183.     See  also  many 
interesting  observations  in  a  small  book  by  Dr  Ord  On  the  infliience  of  colloids 
upon  crystalline  form  and  cohesion. 

3  Phil.  Trans,  for  1855.  179;  and  C.  S.  Journal,  9.  54. 


§§  IQ6,  197]  CHEMICAL   CHANGE.  399 

196.     Harcourt  and  Esson1  examined  two  chemical  pro- 
cesses, viz. 


(1)  H2O2  +  2KI  +  H2SO4  =  2H2O  +  K2SO4  +  I2;  and 

(2)  K2Mn2 


Their  experiments  shewed  that  the  amount  of  the  first 
change  varied  directly  with  the  quantity  of  iodide  present^ 
other  conditions  remaining  constant.  If  the  quantity  of 
H2SO4  was  made  relatively  large,  then  the  amount  of 
change  varied  with  (i)  the  quantity  of  iodide,  (2)  the  quan- 
tity of  dioxide,  (3)  the  time,  (4)  the  total  volume  of  the 
reacting  substances,  and  (5)  with  'some  function  of  each  of 
'the  other  conditions  under  which  the  change  occurs.'  Among 
these  other  conditions,  the  influence  of  varying  the  quantities 
of  acid,  and  of  varying  the  temperature,  were  examined.  It 
was  found  that  the  change  was  accelerated  in  proportion  to 
the  increase  of  the  quantity  of  H2SO4.  Other  acids  were 
tried,  and  the  conclusion  was  arrived  at  that  each  acid  has  a 
definite  '  acceleration-coefficient.' 

The  reactions  between  permanganic  acid  and  oxalic  acid 
in  presence  of  sulphuric  acid  were  found  to  be  very  complex  ; 
it  appeared  to  be  possible  to  analyse  the  change  into  four 
principal  parts  occurring  simultaneously,  and  the  results 
obtained  pointed  to  the  conclusion  that  for  each  part  of  the 
total  operation  the  statement  held  good  that  '  when  any 
'substance  is  undergoing  a  chemical  change  of  which  no  con- 
'dition  varies  excepting  the  diminution  of  the  changing  sub- 
'  stance,  the  amount  of  change  occurring  at  any  moment  is 
'directly  proportional  to  the  quantity  of  the  substance.' 

197.  Menschutkin  has  studied  the  velocities  and  limits  of 
the  typical  change  which  occurs  when  an  alcohol  and  a 
carbon  acid  react  to  produce  an  ethereal  salt  and  water2. 

Certain  fairly  definite  connections  between  the  molecular 
weights  and  the  structure  of  the  acids  and  alcohols  on  the 
one  hand,  and  the  reaction-values  of  the  change  studied,  on 

1  Proc.  R.  S.  14.  470  :  15.  262  ;  and  C.  S.  Journal,  (2)  5.  460. 

2  For  references,  details  of  the  methods,  and  of  the  plan  adopted  for  stating 
the  results,  see  book  i.  chap.  iv.  par.  157. 


4OO  CHEMICAL   KINETICS.  [§  198,  199 

the  other  hand,  have  been  established  by  Menschutkin. 
Thus,  by  determining  the  velocity  and  limit  of  etherification 
of  the  various  acids  of  the  acetic  series  in  the  reactions  be- 
tween these  acids  and  isobutylic  alcohol,  it  is  shewn  that 
replacement  of  H  in  the  CraH2n+1  group  of  these  acids  is  accom- 
panied by  an  increase  of  the  limit  with  a  decrease  of  the 
velocity.  These  changes  in  the  etherification-values  are  more 
marked  when  secondary  acids  are  employed,  and  they  reach 
their  greatest  values  when  tertiary  acetic  acids  react  on 
isobutylic  alcohol. 

When  the  acid  is  unchanged  but  the  alcohol  is  varied,  the 
velocity  of  etherification  up  to  the  point  whereat  equilibrium 
is  established,  increases  by  a  constant  amount  for  each  in- 
crease of  CH2  in  the  molecular  weight  of  the  alcohol  used, 
provided  the  latter  always  belongs  to  the  class  of  normal 
alcohols. 

198.  KajanderV  experiments  on  the  rate  of  evolution  of 
hydrogen  by  the  action  of  various  acids  on  thin  plates  of 
magnesium  shew  that  the  rate  of  this  change  varies  with  the 
temperature,  the  concentration  and  the  nature  of  the  acid 
employed. 

199.  But  in  all  these  cases  the  reaction  chosen  for  ex- 
amination was  so  complicated  that   no  generally  applicable 
conclusions    could   be    deduced.      If  conclusions   as   to   the 
equilibrium   of  chemical   systems   are   to   be   deduced  from 
observations  of  the  velocities  of  changes  undergone  by  these 
systems,  then  the  simplest  changes  must  be  chosen,  and,  if 
possible,   such    as    are    unmixed   with    subsidiary   physical 
operations. 

One  general  conclusion  appears  fairly  deducible  from  the 
experiments  of  those  chemists  whose  work  has  been  referred 
to  in  this  section,  namely,  that  each  chemical  substance  which 
forms  a  member  of  any  changing  system  exerts  a  specific 
action  on  the  course  of  the  changes  which  that  system  under- 
goes2. 

1  Abstracts  in  Ber.  14.  2053  and  2676  (original  papers  are  in  Russian). 

2  See  post>  chap.  ill.  pars.  -223  and  227.    The  more  important  memoirs,  besides 
those  already  referred  to,   on  the  subject  of  this  chapter  are  as  follows  :  BER- 


CHAPTER   III. 
AFFINITY. 


Introductory. 

200.  FROM  the  beginning  of  the  eighteenth,  until  the 
early  years  of  the  present  century,  chemists  busied  them- 
selves with  constructing  tables  of  affinity.  The  conception 
which  found  expression  in  these  tables  was  of  the  same  kind  as 
underlies  such  terms  as  relationship,  kinship,  &c.  As  there 
are  degrees  of  relatedness,  so,  it  was  said,  there  are  degrees  of 
arBnity.  The  same  substance  exhibits  different  degrees  of 
affinity  according  to  the  nature  of  the  other  substances  with 
which  it  reacts.  When  potash  is  heated  with  salammoniac, 
ammonia  is  produced,  but  when  sand  or  silica  is  heated  with 
the  same  salt  there  is  no  change ;  this,  said  Glauber,  is  because 
the  potash  'loves  and  is  loved  by'  the  acid  in  the  salammoniac. 

Geoffrey,  in  1718,  drew  up  tables  of  affinity  of  which  the 
following  is  a  specimen. 


ACIDS  IN  GENERAL. 
fixed  alkali, 
volatile  alkali, 
absorbent  earth, 
metals. 


SULPHURIC  ACID. 
oily  principle  (phlogiston], 
fixed  alkali, 
volatile  alkali, 
absorbent  earth, 
iron, 
copper, 
silver. 


NITRIC  ACID. 
iron, 
copper, 
lead, 
mercury, 
silver. 


THOLLET,  Statique  Chimique  1.  409  et  seq.  WILLIAMSON,  Proc.  R.  S.  16.  72. 
HURTER,  Chem.  News  22.  193.  VAN'T  HOFF,  Ber.  10.  669 ;  see  also  his  Etudes 
de  Dynamique  Chimique  (1884).  POTILITZIN,  Ber.  12.  2370.  LEMOINE,  Ann. 
Chim.  Phys.  (5)  12.  145.  HOOD,  Phil.  Mag.  (5)  6.  371  :  8.  121 :  13.  419.  BER- 
THELOT,  Essai  de  Mec.  Chimique  2.  13,  58,  92,  &c.  HELL  and  URECH,  Ber.  13. 
531.  The  researches  of  Guldberg  and  Waage  and  of  Ostwald  are  considered  in 
detail  in  chap.  ill. 

M.  C.  26 


4O2  CHEMICAL  KINETICS.  [§  2OO 

Each  substance  was  said  to  have  a  greater  affinity  than 
those  which  came  after  it  for  the  compound  at  the  head  of 
the  column.  Thus  a  compound  of  sulphuric  acid  and  copper 
would  be  decomposed  by  the  action  of  iron,  or  of  any  other 
substance  placed  above  copper  in  the  column  headed  sulphuric 
acid. 

But  it  was  gradually  found  that  more  than  a  single  table 
was  required  for  each  substance,  because  the  affinity  of  any 
substance  for  any  other  was  not  the  same  at  all  temperatures, 
and  it  also  varied  according  as  the  reacting  substances  were 
solids  or  in  solution.  In  1775  Bergmann  constructed  tables 
of  affinity  for  59  substances,  two  for  each,  one  representing 
the  affinities  at  low  temperatures  when  the  substances  reacted 
in  solutions,  and  the  other  the  affinities  between  the  solid 
substances  at  high  temperatures.  Bergmann's  table  for 
potash,  for  instance,  was  constructed  thus ; 

POTASH. 

Wet  way.  Dry  way. 

Sulphuric     acid  Phosphoric    acid 

Nitric  „  Boric  „ 

Hydrochloric  „  Arsenic  „ 

Phosphoric      „  Sulphuric  „ 

Arsenic  „  Nittic  „ 

Acetic  „  Hydrochloric  „ 

&c.     &c.  &c.     &c. 

Bergmann  also  fully  recognised  that  each  constituent  of 
any  reacting  substances  exhibits  affinity  for  each  constituent 
of  the  other  substances.  This  point  was  more  fully  insisted 
on  in  the  tables  of  Guyton  de  Morveau  (1786),  of  which  the 
following  is  an  example. 

SULPHURIC  ACID.         NITRIC  ACID.     HYDROCHLORIC  ACID.      ACETIC  ACID. 

Baryta  66  62  36  29 

Potash  62  58  32  26 

Soda  58  50  28  25 

Lime  54  44  20  19 

Ammonia  46  38  14  20 

Magnesia  50  40  16  17 

Alumina  40  36  10  15 


§  201]  AFFINITY.  403 

These  numbers  were  not  given  as  truly  measuring  affinities ; 
but,  it  was  said  that  the  sum  of  the  affinities  of  the  products 
of  a  reaction  is  always  greater  than  the  sum  of  the  affinities 
of  the  original  substances.  Thus,  barium  acetate  is  decom- 
posed by  potassium  sulphate  with  the  production  of  barium 
sulphate  and  potassium  acetate.  Now  the  affinity  of  baryta  for 
acetic  acid  is  represented  in  the  table  by  the  number  29,  and 
that  of  potash  for  sulphuric  acid  by  62  :  but  the  numbers 
representing  the  affinities  of  barium  for  sulphuric  acid  and 
potash  for  acetic  acid  are  66  and  26  respectively  ;  hence 
29  +  62  =  91,  but  66  +  26  =  92. 

Bergmann  regarded  the  relative  quantities  of  acids  needed 
to  neutralise  a  given  quantity  of  base  (or  vice  versa)  as 
measures  of  the  affinities  of  the  acids  for  that  base.  Thus  he 
said  that  100  parts  by  weight  of  potash  are  neutralised  by 
/8J  parts  of  sulphuric  acid,  and  by  64  parts  of  nitric  acid  ; 
he  therefore  concluded  that  the  affinity  for  potash  of  sulphuric 
acid  is  greater  than  that  of  nitric  acid. 

The  phenomena  of  affinity  were  regarded  by  Boyle  as  con- 
nected with  the  mutual  attractions  between  the  small  particles 
of  bodies.  Newton  had  adopted  a  similar  view  and  had  more 
especially  insisted  on  the  two-sidedness  of  this  attraction1. 

201.  The  subject  of  affinity  was  regarded  by  Berthollet  (in 
the  Essai  de  Statique  Chimique)  also  from  this  point  of  view. 
The  mutual  attractions  between  the  small  particles  of  bodies 
which  give  rise  to  chemical  phenomena  Berthollet  regarded  as 
probably  of  the  same  kind  as  the  mutual  attractions  which 
occur  between  the  masses  of  bodies.  The  immediate  effect 
of  the  affinity  exerted  by  one  substance  on  another  is  the 
combination  of  these  substances.  'Every  substance/  said 
Berthollet, c  which  tends  to  enter  into  combination  reacts  by 
reason  of  its  affinity  and  its  mass'2. 

But  chemical  action  does  not  depend  solely  on  affinity 
and  mass.  The  physical  states  of  the  bodies,  the  degree  of 
condensation  or  dilatation,  &c.  condition  the  chemical  change; 

1  For  a  full  historical  account  of  affinity  see  Kopp's  Geschichte  der  Chemie  2. 
285—324. 

2  Essai  1.  i. 

26—2 


404  CHEMICAL  KINETICS.  [§  2OI 

'these  are  the  conditions  which,  in  modifying  the  properties 
'of  the  elementary  parts  of  a  substance,  form  what  I  call  its 
'  constitution^ . 

Berthollet  thus  distinguishes  between  chemical  properties 
which  do,  and  physical  properties  which  do  not,  depend 
immediately  on  affinity.  But  at  the  same  time  he  recognises 
the  close  connection  between  these  properties ;  he  even 
speaks  of  different  kinds  of  affinity  of  which  chemical  affinity 
is  one.  As  we  saw  in  chapter  n.  (par.  173),  Berthollet  insists 
on  the  reciprocity  of  all  chemical  actions  ;  even  in  the  case 
of  a  liquid  he  regards  the  small  particles  as  exerting  mutual 
attraction,  or,  as  he  says,  mutual  affinity. 

The  object  of  Berthollet's  Essai  is  to  consider  the  causes 
which  produce  variations  in  the  results  of  chemical  action, 
i.e.  the  product  of  affinity  and  mass. 

It  should,  I  think,  be  especially  noted  that  Berthollet 
recognised  the  possibility  of  reversing  a  chemical  change  by 
varying  the  conditions,  more  especially  the  masses  of  the 
reacting  substances,  under  which  the  change  proceeds.  A 
substance  with  a  small  affinity  for  another,  if  present  in  large 
quantity,  might  decompose  a  compound  of  the  second  sub- 
stance with  another  for  which  the  affinity  of  the  second  sub- 
stance was  comparatively  large.  'The  measure  of  the  affinity 
'proper  to  every  substance  is',  according  to  Berthollet's  view, 
'the  saturation  which  it  is  able  to  produce  with  those  sub- 
' stances  that  can  combine  with  it'.  It  follows  therefore  that, 
that  acid  the  smallest  quantity  of  which  is  needed  to  saturate 
a  given  weight  of  a  base  has  the  greatest  affinity  for  that  base. 
We  must  remember  that  Berthollet2  regarded  chemical  com- 
pounds as  of  no  definitely  fixed  composition,  and  that  he 
therefore  had  not  gained  the  conception  of  equivalent,  or 
combining,  weights.  We  shall  then  see  that  his  statement, 
that  chemical  action  is  proportional  to  the  products  of  the 
masses  and  the  affinities  of  the  acting  substances,  really 
supplies  a  means  for  determining  the  equivalents  of  the 
reacting  substances.  Until  Berthollet's  theory  of  affinity  was 

1  Essai  1.  3.     See  also  ante,  chapter  n.  par.  173. 

2  Essai  1.  535. 


§  202]  AFFINITY.  405 

supplemented  by  the  knowledge  of  the  equivalent  weights  of 
acids,  bases,  and  other  compounds,  it  was  of  necessity  un- 
productive. 

The  theories  of  affinity  which  prevailed  before  Berthollet 
were  all  founded  on  the  assumption,  that,  if  a  substance,  A, 
decomposes  another,  BC,  with  production  of  A  C  and  B,  then 
the  affinity  of  A  for  C  is  greater  than  the  affinity  of  B  for  C. 
Berthollet  declared  this  conclusion  to  be  erroneous.  Whether 
A  shall  or  shall  not  decompose  BC,  depends,  according  to 
Berthollet,  not  only  on  the  affinities  of  A  and  B  for  C,  but 
also  on  the  quantities  of  A  and  BC  which  take  part  in  the 
reaction. 

202.  When  we  come  to  more  recent  times,  it  is  very 
difficult  to  gain  a  clear  conception  of  the  meaning  of  the 
term  affinity1. 

I  think  we  shall  do  well  to  regard  the  subject,  in  the  first 
place,  from  the  dynamical  point  of  view,  as  far  as  possible 
apart  from  any  theory  of  the  structure  of  matter. 

The  compounds,  AB  and  CD,  react  to  produce  two  new 
compounds,  AC  and  BD\  there  is  mutual  action  and  reaction. 
Looking  at  the  transaction  from  one  side  only,  we  may  say 
that  AB  exerts  force  on  CD,  or  CD  on  AB.  Now  this  force 
may  be  measured ;  (i)  by  finding  the  acceleration  imparted 
to  the  acting  masses  of  AB  or  CD,  i.e.  practically,  by  measur- 
ing the  velocity  of  the  chemical  change  ;  or  (2)  by  arranging 
the  conditions  so  that  the  new  compounds,  A  C  and  BD,  are 
free  to  act  and  react,  in  which  case  AC  will  exert  force  on 
BD,  and  BD  on  A  C,  the  final  result  being  the  establishment 
of  equilibrium  in  the  whole  system.  By  determining  the 
masses  of  AB,  CD,  AC,  and  BD,  present  when  this  equi- 
librium is  established  we  shall  have  the  data  for  finding  the 
ratio  of  the  force  tending  to  change  AB  and  CD  into  A  C 
and  BD,  to  the  force  tending  to  change  A  C  and  BD  back 
into  AB  and  CD2. 

1  See,  for  instance,  the  article  '  Affinity '  in  Watts's  Dictionary,  vol.  I. 

2  The  dynamical  expressionsjfora7,  velocity,  &c.,  are  used  here  and  throughout 
the  paragraphs  dealing  with  affinity  in  senses  not  strictly  accurate,  and  which  vary 
somewhat  from  time  to  time.     This  is  especially  marked  in  some  of  the  quotations 


406  CHEMICAL  KINETICS.  [§  2O2 

But  the  question  of  affinity  may  be  approached  from 
another  point.  When  actions  and  reactions  between  the  parts 
of  a  material  system  are  attended  with  changes  in  the  con- 
figuration of  the  system,  these  actions  and  reactions  are  also 
attended  with  changes  in  the  form  and  the  distribution  of 
the  energy  of  the  system.  Hence,  measurements  of  the 
losses  or  gains  of  energy  of  a  chemical  system  under  defined 
conditions  may  furnish  data  from  which  comparative  esti- 
mates may  be  deduced  of  the  mutual  actions  between  members 
of  that  system.  Measurements  of  the  quantities  of  heat 
evolved  or  absorbed  during  definite  chemical  changes  appear 
to  afford  the  easiest  means  of  measuring  gains  or  losses  of 
energy,  and  in  this  way  of  the  comparative  magnitudes  of 
the  affinities  of  different  substances. 

But  before  we  can  hope  to  gain  exact  measurements  of 
affinity,  we  must  have  a  clear  conception  of  what  it  is  we 
want  to  measure.  Affinity,  I  think,  is  usually  regarded  as  an 
action,  or  sometimes  as  the  cause  of  an  action,  of  some  kind, 
which  occurs  between  the  atoms  of  chemical  elements,  such 
action  resulting  in  a  loss,  or  gain,  of  energy  to  the  system  of 
which  these  atoms  are  the  constituents.  Now  it  is  possible 
that  chemical  affinity  may  be  analogous  to  electrical  po- 
tential ;  that  as  the  existence  of  a  difference  of  electrical 
potential  between  two  particles  implies  the  possibility  of 
electrical  work  being  done,  so  the  existence  of  what  might 
perhaps  be  called  chemical  potential  between  two  atoms 
means  the  possibility  of  chemical  work  being  done.  If  this 
supposition  were  adopted,  we  should  look  to  electrical 
methods  for  the  means  of  investigating  chemical  affinity. 

To  sum  up.  We  may  regard  affinity  as  essentially  con- 
nected with  interatomic,  and  perhaps  intermolecular,  actions ; 
and  we  may  attempt  to  obtain  measurements  of  different 
affinities  by  electrical  methods  :  or  we  may  be  content  to 
connect  the  term  affinity  with  the  actions  and  reactions  which 

from  the  memoirs  of  Guldberg  and  Waage.  But  it  is  almost  impossible  to  do 
otherwise,  unless  one  were  to  invent  a  series  of  new  terms.  To  do  this  would,  I 
think,  be  less  advisable  than  to  employ  the  terms  in  common  use  even  if  the 
meanings  attached  to  them  are  less  precise  than  could  be  wished. 


§  203]  AFFINITY.  407 

occur  when  two,  or  more,  chemically  distinct  substances  com- 
bine to  form  new  substances ;  and  we  may  seek  to  deduce 
measurements  of  these  actions,  either  from  the  velocities  of 
the  chemical  changes,  or  from  the  conditions  of  equilibrium  of 
the  changing  systems,  or  from  observations  of  the  changes  of 
the  energies  of  the  reacting  bodies. 

The  more  important  attempts  which  have  been  made  to 
solve  the  problems  of  affinity  may  all,  I  think,  be  classed 
under  these  headings.  Most  important  work  has  been  done  by 
Guldberg  and  Waage,  and  by  Ostwald,  in  framing  and  ap- 
plying a  theory  of  affinity  founded  on  measurements  of  the 
velocities  of  chemical  changes,  and  of  the  conditions  under 
which  equilibrium  is  attained  by  given  systems. 

Berthelot  and  Thomsen  have  devoted  themselves  chiefly 
to  the  thermal  aspects  of  the  subject.  Helmholtz,  follow- 
ing on  the  older  work  of  Berzelius,  Faraday,  Joule,  and 
Thomson,  has  recently  made  some  advances  in  applying 
electrical  methods  to  these  questions. 


SECTION  I.      The  Theory  of  Guldberg  and  Waage. 

203.  We  have  seen  how  much  Berthollet  insisted  on  the 
importance  of  considering  the  relative  masses  of  the  reacting 
substances  which  take  part  in  every  chemical  change.  It  is 
to  this  special  part  of  the  general  question  of  affinity  that 
Guldberg  and  Waage  have  chiefly  devoted  themselves1. 

Berthollet's  statement  "Toute  substance  qui  tend  a  en- 
'  trer  en  combinaison  agit  en  raison  de  son  affinite  et  de  sa 
'quantite"  (Essai\.  2),  has  been  extended  and  rendered  more 
exact  by  the  researches  of  these  naturalists.  They  thus  ex- 
press themselves :  "  Suppose  that  two  bodies,  A  and  B,  can 
'be  converted,  by  double  decomposition,  into  A'  and  B\ 
'and  that  A1  and  B'  can  be  reconverted,  under  similar  con- 
'  ditions,  into  A  and  B ;  neither  of  these  changes  will  be  com- 
'  plete.  At  the  close  of  the  reaction  there  will  always  be 
'present  four  bodies,  A,  By  A  and  B' ;  and  the  force  which 

1  Ettides  sur  les  Affinites  Chimiques  (Christiania,  1867),  *&&.  Journal  fur  prate* 
Chemie  (2)  19.  69. 


408  CHEMICAL  KINETICS.  [§  203 

'brought  about  the  formation  of  A'  and  B'  will  be  held  in 
'equilibrium  by  the  force  which  caused  the  formation  of 
'  A  and  B.  The  force  which  caused  the  formation  of  A'  and 
'  B'  increases  in  proportion  to  the  coefficient  of  affinity  of  the 
'reaction  A+B  =  A'  +  B',  but  it  is  also  dependent  on  the 
'  quantities  of  A  and  B.  We  have  found  that  this  force  is 
4  proportional  to  the  product  of  the  active  masses  of  A  and  B. 

*  Representing  the  active  masses  of  A   and  B  by  /  and  q 
'  respectively,  and  the  coefficient  of  affinity  by  k,  we  have  the 
'force  —k.p.q  .......    If  the  active  masses  of  A'  and  B'  be 

'/  and  q'  respectively,  and  the  coefficient  of  affinity  of  the 
'  reaction  A  +  B'  =  A  +  B  be  k't  then  the  force  which  tends  to 
'  bring  about  the  re-formation  of  A  and  B  is  equal  to  k  .p'  .  q'  . 

*  As  this  force  is  held  in  equilibrium  by  the  other,  we  get  the 
'  equation  of  equilibrium 


'By  experimentally  determining  /,  q,  p'  and  q,  the  ratio 
'  k  :  k'  can  be  calculated  ;  on  the  other  hand,  if  this  ratio  has 
'  been  determined,  it  is  possible  to  calculate  the  result  of  the 
'  reaction  for  any  initial  condition  of  the  four  substances.  If 
'  P,  Q,  P'  and  Q  represent  the  number  of  molecules1  of 
1  A,  B,  A'  and  B'  present  before  the  action  begins,  and  if  x 
'represents  the  number  of  molecules  of  A  and  B  transformed 
'into  A  and  B',  and  if  we  suppose  that  the  total  volume 
'remains  constant  during  the  reaction,  and  is  equal  to  V, 
'then 


y 


'  Substituting  these  values  for  /,  &c.  in  the  equation  of  equi- 
'librium,  and  multiplying  by  Vz,  we  get 


'  The  value  of  x  is  easily  found  by  the  help  of  this  equa- 
tion2." 

1  In  the  original  the  expression  is  les  quantites  absolues  ;  but  it  is  evident  from 
other  parts  of  the  memoir  (e.g.  p.  54)  that  this  means  the  number  of  molecules. 

2  Etudes,  pp.  6,  7. 


§  204]  AFFINITY.  409 

The  active  mass  of  a  substance  is  defined  as  the  quantity 
of  that  substance  in  unit  volume  of  the  chemical  system 
which  undergoes  change ;  all  the  substances  being  present 
in  the  ratios  of  their  equivalent  weights.  The  symbols 
/  and  q  therefore  represent  certain  numbers  of  equivalents 
of  A  and  B. 

The  value  of  the  coefficient  of  affinity  of  a  reaction  de- 
pends upon  the  nature  of  the  reacting  substances  and  on  the 
temperature. 

Inasmuch  as  the  ratio  k/k'  is  determined  by  a  method  of 
equilibrium,  the  chemical  changes  selected  must  be  such  as 
are  composed  of  two  equal  and  opposite  actions.  Such  a 
change  is  that  which  occurs  when  alcohol  and  acetic  acid 
react  to  produce  ethylic  acetate  and  water ;  after  a  time  the 
action  stops,  and  the  system,  alcohol,  acetic  acid,  ethylic 
acetate,  and  water,  remains  in  equilibrium.  Moreover  as  the 
theory  regards  only  the  forces  which  are  concerned  in  the 
production  of  the  new  compounds,  and  the  re-formation  of 
the  original  compounds,  the  reactions,  from  a  study  of  which 
the  value  of  kjk  is  to  be  deduced,  must  be  as  simple  as 
possible,  in  other  words  they  must  be  as  free  as  possible  from 
all  secondary  actions.  There  should  be  one  definite  chemical 
change,  and  one  only. 

204.  That  we  may  have  a  clear  conception  of  the  mean- 
ing given  by  Guldberg  and  Waage  to  the  expression  coefficient 
of  affinity,  let  us  hear  what  they  themselves  say. 

"  In  a  simple  decomposition  of  the  form  AB  +  C=  AC+By 
'  the  formation  of  A  C  is  chiefly  brought  about  by  the  attraction 
'between  A  and  C\  but  there  are  also  attractions  between 
'  the  other  substances,  and  the  force  which  causes  the  forma- 
tion of  AC  is  the  resultant  of  all  these  attractions.  This 
'force  may  be  regarded  as  constant  for  a  definite  tempera- 
'  ture ;  we  represent  its  amount  by  k,  which  we  call  the 
'  coefficient  of  affinity  for  the  reaction  in  question.  In  the 
*  same  way,  in  the  double  decomposition,  AB  +  CD  —  A  C+  BDy 
'  the  force  which  causes  the  formation  of  the  new  substances 
'is  a  function  of  all  the  attractions  between  the  bodies  A,  B, 


410  CHEMICAL  KINETICS.  [§  204 

'  C,  D,  AB,  CD,  AC,  and  BD,  and  the  resultant  force,  k,  is  the 
'  coefficient  of  affinity  for  the  reaction1." 

"When  the  coefficient  [of  affinity]  is  equal  to  zero,  or  is 
'  negative,  no  action  can  proceed,  but  it  must  not  be  concluded 
'  that  when  no  action  occurs,  the  coefficient  of  affinity  is  equal 
1  to  zero.  .  .  .    There  are  other  causes  which  tend  to  stop  the 

'  reaction.     Besides  A  and  B,  there  may  be  other  bodies  in 
'the  sphere  of  action,  X,    Y,  Z,  &c.;   these  we  call  foreign 
1  bodies  (les  corps  etr  angers).      Between  these  and  A  and  B, 
'and  also  between  these  themselves,  there  are  chemical  at- 
'  tractions,  which   manifest  themselves  as   forces   tending   to 
'accelerate  or  retard  the  action  between  A  and  B.     These 
'attractions  are  of  the   same   nature  as  the  true  forces  of 
1  affinity  ;  probably  they  follow  the  same  laws.     We  suppose 
'  that  the  force  produced  in  the  action  between  A  and  X,  and 
'  affecting  the  reaction  between  A  and  B,  is  proportional  to  the 
'  product  of  the  active  masses  of  A  and  X,  and  a  coefficient,  a, 
'  called  by  us  the  coefficient  of  action.     In  the  same  way  may 
'  be  represented  the  action  between  each  of  the  other  bodies, 
'as  regards  A  and  B.     Finally  the  mutual  actions  between 
'the  foreign  bodies  must  be  regarded.     The  attraction  be- 
'  tween  X  and  Y  will  produce  a  force,  represented  as  aX  Y, 
'which  tends  to  accelerate  or  retard  the  action  between  A 
'  and  B.     The  same  holds  good  for  X  and  Z,  &c.     The  total 
'force  causing  the  action  between  A  and  B  is  the  resultant  of 
'all  these  actions,  and  is  equal  to  the  sum  of  all  the  forces 
'  we  have  to  determine.     Representing  the  active  masses  of 
'  A,B,X,  Y,  Z  .....  .  by/,  q,  X,  Y,Z,  ......  the  total  force,  T,  is 

'  expressed  by  the  equation 


'The  coefficients  of  action,  a,  b,c,  ......  depend  on  the  nature 

'of  the  substances  and  the  chemical  reaction  .......    When  the 

'  coefficient  of  action  is  positive,  the  force  to  which  it  corre- 
'  sponds  tends  to  accelerate  the  chemical  reaction,  and  when 
'the  coefficient  is  negative,  the  force  tends  to  retard  the  re- 
'  action  ......  As  a  rule  the  coefficients  of  action  are  small 

1  Etudes,  p.  6. 


§§  205,  2°6]  AFFINITY.  41! 

'compared  with  the  coefficients  of  affinity,  and  as  a  con- 
'  sequence  the  total  force  is  usually  positive,  and  the  sub- 
'  stances  A  and  B  undergo  change  into  A'  and  jB'1." 

205.  Assuming  that  a  chemical  change  proceeds  during 
a  sensible  time,  which  varies  for  each  change,  it  is  possible  to 
determine  the  affinity-coefficients  from  measurements  of  the 
velocity  of  the  change.     An  attempt  is  made  (Etudes,  pp.  10, 
n)  to  develop  the  necessary  formulae  from  the  equations 

v=$T,  and  v  =  $(T-T'\ 

where  v  =  the  velocity  of  the  change  (i.  e.  the  quantity  of 
A1  +  B'  produced  from  A  +B  in  unit  time),  and  <f>  is  a  factor 
called  by  Guldberg  and  Waage  the  coefficient  of  velocity ;  T 
being  the  total  force  when  A'  and  B'  do  not  react  to  re- 
produce A  and  B ;  and  T'  being  the  total  force  tending 
to  reproduced  and  B  in  those  cases  where  A'  and  Bf  do  react 
on  each  other. 

206.  There  are  two  general  methods  by  which  the  theory 
may  be  tested ;  in  both  cases  it  is  necessary  to  arrange  the 
experimental  conditions  so  that  the  forces  of  action  may  be 
reduced  as  nearly  as  possible  to  zero. 

I.  Let  there  be  four  bodies  A,  B,  A',  and  B ',  with  the 
active  masses/,  q,p' ,  and  q\  let  the  coefficient  of  affinity  for 
the  reaction  A  +  B  =  A'  +  B  be  £,  that  for  the  reaction 
A  +  B'  =  A+B  be  £',  and  let  the  coefficients  of  action  for 
A  and  A'y  A  and  B>  B  and  A',  B  and  B,  be  a,  b,  c,  and  d, 
respectively,  and  the  coefficients  of  action  for  A'  and  A, 
B'  and  A,  A'  and  By  B'  and  B,  be  a,  b' ,  c,  and  d',  respectively, 
then  the  total  force  for  the  reaction  between  A  and  B  is 

T=  kpq  +  app'  +  bpq'  +  cqp'  +  dqtf. 
And  the  total  force  for  the  reaction  between  A'  and  B  is 

T = k'p'q'  +  a'p'p  +  b'q'p  +  Sp'q + d'q'q. 

When  equilibrium  is  established  T=T'\  then  putting 
a'-a  =  a,  &-&=&,  c'-c=y,  d'-d=$, 

1  £tudes,  pp.  8,  9.  On  p.  9  it  is  shewn  that  an  equation  of  equilibrium  can 
be  obtained  in  which  all  the  coefficients  of  affinity  and  the  coefficients  of  action 
are  represented.  See  next  page. 


412  CHEMICAL  KINETICS.  [§  2O6 

the  equation  of  equilibrium  becomes 


Then  treating  this  equation  in  the  same  way  as  the  more 
simple  equation  kpq  =  k'p'q'  was  treated  on  p.  408,  an  expres- 
sion is  obtained1  by  the  use  of  which  the  amounts  of  A  and  B 
transformed  into  A'  and  B'  when  equilibrium  is  reached  may 
be  calculated  for  any  initial  system  of  the  four  bodies  A,  B, 
A'  and  B. 

s> 

This  equation  is  applied  (Etudes,  pp.  53  —  55)  to  the 
system,  acetic  acid,  alcohol,  ethylic  acetate,  and  water.  The 
following  numbers  shew  the  close  agreement  between  the 
observed  and  the  calculated  values  of  f,  i.e.  the  quantities  of 
alcohol  and  acid  transformed  into  ethylic  acetate  and  water 
when  equilibrium  is  established. 

VALUES  OF  £. 

SERIES  I.  Q  Observed.  Calculated. 

One  molecule  acid+  i  0*665  0*668 

Q  molecules  alcohol.  i  '5  0*779  0*772 

2  0*828  0*827 

2*8  0*856  0*870 

3  0*882  0*878 

12  0*932  O*93O 

500  i  *ooo  i  *ooo 

SERIES  II.  P 

One  molecule  alcohol  +                i  0*665  0*668 

P  molecules  acid.                          2  0*858  0*856 

5  0*966  0972 

1  Let  P,  Q,  P',  and  Q  represent  the  numbers  of  molecules  of  A,B,  A',  and  B', 
respectively,  before  the  reaction  begins,  and  let  £  represent  the  limit,  or  the  quan- 
tities of  A  and  B  transformed  into  A'  and  B't  then  the  active  masses  of  the  four 
substances  are  given  by  the  equations 


where  v  =  total  volume.  Substituting  these  values  in  the  equation  of  equilibrium 
given  in  the  text,  and  multiplying  by  v2,  the  expression  referred  to  in  the  text  is 
obtained,  viz. 


§  206]  AFFINITY.  413 

SERIES  III.  P  Observed.  Calculated. 

One  mol.  acid+  o  0*665  0*668 

one  mol.  alcohol  +  0*13  0*626  0*648 

P  mols.  ethyl  acetate.  0*85  0*563  0*550 

1*6  0*521  0-487 

SERIES  IV.  Q 

One  mol.  acid+                             o  0*882  0*878 

three  mols.  alcohol  +                      I  0*809  0*803 

Q'  mols.  water.                               2  0*739  0*744 

8  .          0*468  0*512 

If  A  and  A'  are  solid  bodies,  while  B  and  B'  are  liquids, 
then  the  active  masses  of  A  and  A'  remain  practically  con- 
stant throughout  the  reaction ;  if  these  masses  are  made 
equal,  then  the  equation  given  on  p.  408  for  finding  ;r  becomes 


and 


When  the  coefficients  of  action  are  taken   into   account,   a 
modified  form  of  this  equation  is  easily  obtained,  viz. 


when  X,  //,  and  v  are  constants1.     From  this  the  values  of  f 
can  be  determined  by  interpolation. 

As  examples  of  the  application  of  the  equation  of  equi- 
librium to  systems  containing  solids  we  may  take  a  few 
numbers  from  the  tables  on  pp.  59  and  60.  The  action 
studied  is  that  of  the  alkaline  carbonates  on  barium  sulphate  ; 
A  —  barium  sulphate,  B  =  alkaline  carbonate,  A'  =  barium 
carbonate,  B  —  alkaline  sulphate. 

VALUES  OF  |. 

SERIES  I.  Q  Observed.  Calculated. 

i  mol.  barium  sulphate  +  3*5  0*719  0*715 

500  mols.  water  (at  ioo°)+  2*5  0*500  0*500 

Q  mols.  potassium  carbonate.        2  o'395  0*391 

i  0*176  0*178 

1  £tudes,  p.  59. 


414  CHEMICAL  KINETICS.  [§§  2O7,  2O8 

SERIES  II.  Q  Q  Observed.  Calculated. 

i  mol.  barium  sulphate  +  2  0*25          0*200             0*198 

500  mols.  water  (at  100°)  +  3  0*25          0*408              0*409 

Q  mols.  potassium  carbonate  +  2  0*50          o*  trace          o'ooo 
Q'  mols.  potassium  sulphate. 

II.  The  theory  may  also  be  tested  by  calculating  the 
quantities  of  the  new  substances  A'  and  B'  produced  from  A 
and  B  in  a  given  time,  by  the  help  of  formulae  obtained  by 
developing  the  two  equations  already  given  as  expressing  the 
velocity  of  a  reaction,  viz.  v  =  $T\  and  v—$(T—  T').  This 
is  done  for  the  system  alcohol  +  acetic  acid,  &c.,  and  for  the 
system  barium  sulphate  +  alkaline  carbonate,  &c.  (Etudes, 
pp.  55 — 58;  and  60 — 61).  The  formulae  are  complicated; 
the  observed  results  agree  very  well  with  the  calculated 
numbers1. 

207.  Having  established  their  theory  by  the  experiments 
and  calculations  detailed  in  their  first  memoir,  Guldberg  and 
Waage   proceed   to   apply  it  to  various  classes  of  chemical 
reactions2.     Formulae,  obtained  from   the   two   fundamental 
equations 

(i)k.p.q=k'.p'.q'    and    (2)*=0(7--n 

are  applied  to  calculate  the  amount  of  change  when  equilibrium 
is  established  in  systems  consisting  of  (a)  four  soluble  sub- 
stances, (b)  two  soluble  and  two  insoluble  substances,  (c)  an 
indefinite  number  of  soluble  substances,  (d)  gaseous  sub- 
stances arising  from  the  dissociation  of  a  solid,  and  (e)  gaseous 
substances  only8. 

208.  In  applying  the  theory  to  systems  containing  gaseous 
constituents,  and  more  especially  to  systems  undergoing  dis- 
sociation, it  is  almost  necessary  that  some  hypothesis  should 
be   adopted  regarding  the  mechanism  of  chemical  change. 
The   hypothesis   adopted    by   Guldberg    and   Waage   is   es- 
sentially the  same  form  of  the  molecular  and  atomic  theory 
as  has  been  applied  by  Pfaundler  to  the  subject  of  chemical 

1  But  see/0.tf,  par.  221. 

2  Journal fur  prakt.  Chemie  (2)  19.  69. 

3  For  details  see  the  original  paper,  loc.  cit.,  or  the  condensed  translation  in 
Phil.  Mag.  (5)  8.  181. 


§  209]  AFFINITY.  415 

equilibrium  in  general1.  In  an  apparently  homogeneous 
molecular  system  there  must  always  be  many  molecules  in  a 
condition  more  or  less  divergent  from  the  mean  state  of  the 
system.  Let  the  molecules  of  two  substances  which  act 
chemically  on  one  another  be  represented  by  A  and  B\  let 
these  molecules  be  composed  of  the  atoms  (or  atomic  groups) 
aa,  and  bb,  respectively,  performing  certain  vibrations  within 
the  molecules  A  and  B.  At  certain  points  in  these  vibrations 
the  force  between  a  and  a,  and  between  b  and  b  will  be  at  a 
minimum  ;  if  at  this  moment  A  and  B  approach  each  other, 
chemical  action  will  occur  with  the  production  of  new  mole- 
cules, C,  composed  of  the  atoms  ab.  If  the  number  of 
molecules  of  A  which  are  in  this  condition  of  readiness  to 
undergo  change  be  a',  the  total  number  of  molecules  of  A  in 
unit  volume  of  the  system  being  a,  and  if  the  number  of 
molecules  of  B  ready  to  undergo  change  be  /3',  the  total 
number  of  molecules  of  B  being  /3,  then  the  velocity  of 
formation  of  the  new  molecules,  Cy  may  be  represented  by 
the  equation  <f> .  aafift'  =  kafi,  when  k  =  $a'/3'.  The  factor  <f> 
depends  on  the  temperature,  and  the  chemical  nature  of  the 
substances  A  and  B ;  the  nature  of  this  dependence  must  be 
experimentally  determined.  An  expression,  similar  to  that 
given,  can  be  found  for  the  velocity  of  re-formation  of  A  and 
B ;  and  hence  the  amounts  of  Ay  B,  and  C,  which  are  present 
when  equilibrium  is  attained  can  be  calculated  for  any  initial 
state  of  the  system. 

209.  The  application  of  this  method  to  cases  of  dissocia- 
tion is  considered  in  detail  in  Guldberg  and  Waage's  second 
paper2,  where  formulae  are  deduced,  by  the  help  of  the  con- 
siderations sketched  in  the  preceding  paragraph,  for  finding 
the  equilibrium  of  a  gas  which  dissociates  into  two  or  more 
constituents,  along  with  which  a  definite  amount  of  the 
original  gas  is  also  present.  The  formulae  are  applied  chiefly 
to  the  cases  of  nitrogen  tetroxide,  and  hydriodic  acid,  which 
dissociate  when  heated  into  nitrogen  dioxide  (NO2),  and 
hydrogen  and  iodine,  respectively. 

1  See  ante,  chap.  u.  par.  187. 

2  J-fur  prakt.  Chemie(i]  19.  102—114. 


416  CHEMICAL   KINETICS.  [§§2IO,  211 

210.  Guldberg   and    Waage   have   established   the   pro- 
position, that,  when  secondary  actions    are   eliminated,  the 
amount  of  any  chemical  change  is  proportional  to  the  products 
of  the  active  masses  of  the  substances  concerned  and  the 
coefficients  of  affinity  of  the  reaction.     They  have  shewn  that 
the  values  of  the  coefficients  of  affinity  of  various  reactions 
can  be  determined  in  terms  of  the  coefficient  of  one  of  the 
reactions  taken  as  equal  to  unity ;  and  they  have  made  a  few 
determinations  of  these  values.     But  their  object  has  been 
rather  to  establish  a  general  theory  than  to  carry  out  its 
application  in  one  particular  direction.     Moreover  the  reac- 
tions studied  by  Guldberg  and  Waage  are,  for  the  most  part, 
too  complex  for  the  purpose  of  finding  data  from  which  the 
values  of  different  coefficients  of  affinity  may  be    deduced, 
however  admissible   the   reactions   may   be   for   testing   the 
theory  which  these  naturalists  have  proposed. 

This  theory  has  been  applied  to  the  determination  of 
the  relative  coefficients  of  affinity  of  various  changes  by 
Ostwald. 

211.  It  is  necessary  to  eliminate  as  far  as  possible  all 
secondary   actions   from   the   chemical   changes   chosen    for 
study.     When  two  substances  react,  in  solution,  to  form  two 
new  substances,  which  also  remain  in  solution,  we  have  pro- 
bably as  simple  a  case  as  can  be  found  for  applying  Guldberg 
and  Waage's  theory.     But  a  difficulty  arises.     How   is  the 
amount  of  change  to  be  experimentally  determined  ?     Let  A 
and  B  react  to  produce  A'  and  B',  all  the  substances  being 
dissolved  in  water :  if  it  is  attempted  to  determine  the  quan- 
tities of  A'  and  B'  produced,  by  ordinary  analytical  methods, 
e.g.  by  precipitation  as  insoluble  salts,  the  addition  of  the 
necessary  reagents  disturbs  the  equilibrium  of  the  system, 
and  thus  produces  changes  in  the  quantities  of  A,  B,  A'  and 
B'  present,  whereby  any  measurement  of  the  coefficient  of 
affinity  is  rendered  untrustworthy.    It  would  therefore  appear 
that  the  amount  of  chemical  action,  in  a  case  such  as  we  are 
considering,  must  be  determined  by  measuring  the  magnitude 
of  some  physical  constant,  or  constants,  of  the  system,  before 
and  after  the  chemical  operation. 


§  212]  AFFINITY.  417 

The  application  of  physical  measurements  to  the  quanti- 
tative investigation  of  chemical  changes  seems  to  have  been 
first  made  by  Steinheil1  in  1843.  The  thermal  methods  of 
Thomsen,  the  magnetic  methods  used  by  G.  Wiedemann, 
the  chromometric  methods  employed  by  A.  Miiller,  and  the 
volumetric  and  optical  processes  adopted  by  Ostwald,  are 
all  examples  of  the  application  of  the  same  general  con- 
ception2. 

212.  Ostwald  has  sought  to  find  the  relative  affinities  (see 
p.  418,  also  post,  pars.  214-218,  223,  227,  and  235)  of  various 
acids.  The  analytical  method  employed  in  his  earliest  paper 
was  to  measure  the  specific  volumes3  of  aqueous  solutions  con- 
taining equivalent  quantities  of  (i)  acids,  (2)  bases,  and  (3) 
mixtures  of  acids  and  bases4. 

In  the  reaction  A  +  B  =  A'  +  B',  let  A  and  A'  be  two 
acids,  and  B'  and  B  their  neutral  salts  with  the  same  base, 
B'  being  the  salt  of  acid  A,  and  B  the  salt  of  acid  A.  Then 
according  to  Guldberg  and  Waage's  theory  we  have 


From  this,  the  ratio  k'/k  can  be  determined.  If  for  the 
sake  of  simplicity  k'  is  taken  as  equal  to  i//£,  the  equation 
becomes 


1  Annalen  48.  153. 

2  The  more  important  memoirs  on  this  subject  are  these:  K.  HOFMANN,  Pogg. 
Ann.  133.  575.     THOMSEN,  Pogg.  Ann.  138.  65,  and  many  other  papers;  see 
Thermochemische  Untersuchungen,  vol.  I.     KRECKE,  J.  fur  prakt.   Chemie  (i)  3. 
286.    BERTHELOT  and  SAINT-MARTIN,  Ann.  Chim.  Phys.  (4)  26.  433  (and  other 
papers).     A.  MULLER^  Pogg.  Ann.  Erganzsbd.  6.  123.     G.  WIEDEMANN,  J.  fur 
prakt.  Chem.  (2)  9.  145.     DiBBiTS,  Pogg.  Ann.  Erganzsbd.  7.  462.     BOGUSKI 
and  KAJANDER,  Ber.  9.  1646.     GLADSTONE,  Phil.  Trans,  for  1855.  179.     GLAD- 
STONE and  DALE,  Phil.  Trans,  for  1863.  317.     LAN  DOLT,  Pogg.  Ann.  123.  595. 
WULLNER,  Pogg.  Ann.  133.   i.     RUDORFF,  Ber.  6.  482  and  643.     OSTWALD, 
J.  fur.  prakt.   Chemie,   (2)  25.  i.     WIEDEMANN,  Wied.  Ann.  17.  561.     KRUSS, 
fler.lB.  1243:  16.  2,051.     RAOULT,   Compt.  rend.  94.    1517:  95.  1030:  97.  941: 
98.  509,  1047.     Also  Ann.  Chim.  Phys.  (3)  28.  133:  (6).  2..  66. 

3  Specific  volume  =  volume  of  unit  weight  referred  to  water  (at  20°)  as  unity. 

4  Ostwald's  papers  are  to  be  found  in  the  Journal  fiir  prakt.  Chemie.  (2)  16.  385  : 
18.  328:  19.  468  :  22.  251  :  23.  209  and  517  :  24.  486:  27.  I  :  28.  449:  29.  385. 

5  See  ante,  par.  203. 

M.  C.  27 


41 8  CHEMICAL   KINETICS.  [§212 

When  one  acid  reacts  on  the  neutral  salt  of  another,  in 
equivalent  quantities,  then  P=0=i;  P'—Q'  =  o}  and  the 
equation  has  the  form 

£*(!-*)*  =AS,  or  £=^; 

where  ^r  =  the  amount  of  salt  B  decomposed,  and  (\—x)  — 
the  amount  of  salt  B  undecomposed,  by  the  acid  A  ;  or,  as 
equivalent  quantities  are  used,  x  —  amount  of  base  combined 
with  acid  A,  and  (i  —  x]  =  amount  of  base  combined  with 
acid  A'.  Hence,  in  the  reactions  of  two  acids  on  the  neutral 
salt  of  one  of  the  acids,  the  affinity-coefficients  may  be 
defined  as  the  proportions  in  which  the  base  is  shared  (das 
Theilungsverhaltniss  der  Basis]  between  the  two  acids,  when 
the  three  substances  react  in  equivalent  quantities.  'The 
'amount  of  base  combined  with  each  acid  is,  however,  a 
'  measure  of  the  affinity  of  the  acid  for  that  base  ;  the  affinity- 
'  coefficients  therefore  express  the  ratios  of  these  affinities, 
'i.e.  they  express  the  relative  affinities  of  the  acids  for  the 
'base1'.  The  values  of  these  relative  affinities  of  acids 
must  be  determined  for  different  bases  and  at  different  tem- 
peratures. 

When  aqueous  solutions  of  equivalent  quantities  of  acids 
and  bases  are  mixed,  the  volume  of  the  product  is  not  equal 
to  the  sum  of  the  volumes  of  the  constituents.  If  the  tempera- 
ture and  the  concentration  of  the  solutions  are  kept  constant, 
the  change  of  volume  is  found  to  depend  upon  the  nature 
of  the  acid,  and  of  the  base.  In  Ostwald's  experiments  a 
solution  of  normal  concentration  was  one  containing  one  equi- 
valent of  acid,  or  base,  in  grams,  in  1000  grams  of  solution. 
The  temperature  was  20°  C. 

Let  the  change  of  volume  observed  on  mixing  normal 
solutions  of  acid  A  with  base  C  be  represented  by  vt  and  the 
change  when  acid  A'  is  mixed  with  the  same  base,  C,  by  v' \ 
let  both  acids  act  simultaneously  on  the  base,  acid  A  com- 
bining with  x  parts,  and  acid  A'  with  i  —  x  parts  of  the  base, 
then  the  volume-change  in  the  last  reaction,  «/0,  is  made  up 

1  Ostwald,  loc.  cit.  16.  386. 


§  213]  AFFINITY.  419 

of  two  parts,  viz.  that  attending  the  formation  of  x  parts  of 
the  salt  AC,  and  that  attending  the  formation  of  (i  —  x]  parts 
of  the  salt  A'C,  hence 


The  values  of  v  and  v',  and  hence  the  difference  v  —  v',  can 
generally  be  directly  determined  ;  but  in  many  cases  it  is 
preferable  to  determine  the  difference  v  —  v  by  an  indirect 
method. 

The  method  is  given  by  Thomsen1.  If  an  equivalent  of  acid 
A'  is  added  to  the  salt  AC,  and  an  equivalent  of  the  acid  A 
to  the  salt  A'C,  then  the  difference  between  the  observed 
volume-changes  is  equal  to  the  desired  difference  v  —  v.  The 
method  is  founded  on  the  theorem,  that,  in  homogeneous 
solutions  containing  equal  quantities  of  the  same  constituents, 
the  final  arrangement  of  the  constituents  is  the  same  what- 
ever may  have  been  the  initial  arrangement2. 

Representing  the  observed  change  of  volume  when  A  acts 
on  A'C,  by  v±  and  the  change  when  A'  acts  on  AC  "by  v9,  and 
putting  f  as  equal  to  the  sum  of  all  the  secondary  reactions, 
the  equation  already  given  for  finding  x  becomes 

v\-£ 
x=—     *  ;    and  i-;tr=- 

^i  -  V 

213.  As  an  example  of  the  application  of  this  method, 
let  us  glance  at  Ostwald's  first  attempt  to  determine  the 
relative  affinities  of  the  acids  H2SO4,  H2C12,  and  H2N2O6, 
for  the  bases  KOH,  NaOH,  NH4OH,  MgO,  ZnO,  and 
CuO.  The  normal'  solutions  required  were  21  in  number; 
3  for  the  acids,  and  3  for  each  base,  viz.  solutions  of  the 
nitrate,  chloride,  and  sulphate.  The  Volume'  of  each  solution, 
i.e.  the  volume  which  contained  one  gram-molecule  of  the 
acid  or  salt,  was  determined  at  20°,  and  then  the  expansion 
of  the  liquid  was  found  by  experiment  for  the  interval  o°  —  60°; 
the  'volume'  at  any  temperature  between  o°  and  60°  could  then 
be  calculated.  Besides  determining  the  'volumes'  of  the 
original  solutions,  and  of  the  solutions  obtained  by  mixing  the 

1  Fogg.  Ann.  138.  86. 

-  This  is  experimentally  proved  to  be  correct. 

27—2 


420  CHEMICAL   KINETICS.  [ 

various  acids  and  salts,  it  was  necessary  to  measure  the 
volume-change  (if  any)  which  occurred  when  a  given  acid 
was  mixed  with  the  solution  of  its  own  neutral  salt,  in  order 
to  find  data  for  calculating  the  value  of  f  in  the  equation  to 
be  afterwards  employed.  The  results  are  tabulated  as  follows. 

7/x= volume-change  attending  the  action  of  nitric  acid,  or  hydrochloric 

acid,  on  sulphates ; 
vz= volume-change  attending  the  action  of  sulphuric  acid  on  chlorides 

or  nitrates. 

Nitric  against  sulphuric  acid.  Hydrochloric  against  sulphuric  acid. 


Base. 

*ii 

^2 

; 

^i  -  v2  ; 

*v» 

^2; 

vl  -  vz 

Potash 

+  14*00 

-2 

•38 

+  16-38 

+  13*08 

-2-09 

+  15-17 

Soda 

+  1377 

-2 

73 

+  16-50 

+  13-00 

-2-52 

+  15-52 

Ammonia 

+  1  1*64 

-2 

70 

+  14-34 

+  11-45 

-278 

+  14-23 

Magnesia 

+  10-58 

+  13-64 

+  10-47 

-3-05 

+  13-52 

Zinc  oxide 

+  8-86 

-3 

•ii 

+  II-97 

+  9-08 

-3-32 

+  12-40 

Copper  oxide 

+  7-85 

-3 

•42 

+  11-27 

+  8-06 

-3-49 

+  11*55. 

The  volume-changes  attending  secondary  reactions  were 
also  measured  and  tabulated.  The  sum  of  these  secondary 
reactions,  f,  is  made  up  of  the  parts 


and  ;rRN2O6  +  (i  -;r)H2N2O6  [or  ;rRCl2  +  (i  - x)  H2C12]. 

The  change  of  volume  attending  the  last  of  these  reactions 
was  found  to  be  equal  to  zero. 

214.     From  these  data  the  value  of  x  is  found  for  each 

TJ    —  ^" 

base  and  pair  of  acids  by  the  equation  x  =  —     -  ;     and   from 

these  values  the  relative  affinities  of  each  pair  of  acids  for 
each  base  are  calculated.     The  relative  affinities  are  those  of 
1-T  N"  O  "FT  fl  TT  f  1 

W    ~H^n~6>  (2)    TT  on  *  and  (3)    *H--M~n~-    Thefirstand 

n.2ow4  n.2ow4  n.2iM2w6 

second  are  calculated  by  help  of  the  equation  k  =  ~— ,  and 

the  third  is  obtained  indirectly  by  dividing  the  second  by 
the  first,  the  value  of  the  difference  vv  —  v^  being  too  small  in 
this  case  to  allow  of  a  trustworthy  result  being  obtained  by 


AFFINITY. 


42I 


direct  calculation.     The  following  table  exhibits  the  relative 
affinities  of  the  three  pairs  of  acids. 


Base.            l 

.      H2N206 
H2SO4  ' 

Potash 

°'667_ 

—  *£  CKJ 

o-333 

Soda 

0-667 

^  =  2'00 
0-333 

Ammonia 

°'652       r-88 
-=  I  oo 

0-348 

Magnesia 

0*638 

0-362  ""-1  7 

Zinc  oxide 

0-617     , 

0^383- 

Copper  oxide 

0-591 

—  T  '  1  1 

0^09 

RELATIVE  AFFINITIES. 


H2C12 
H2S04* 

°'659  =  rc 
0-341 

°'657==I, 

o'343 


in. 


92 


H2N 
i'94  = 

2-00 

r92  = 

2 '00 

r8 1 


i<V 

=0-97 

=0-96 


0-356 


0-605 


r6i 


0-416 


=  1*40 


i  -40 

T.T 

i  44 


.T  =0-97- 


215.  The  ratio  of  the  affinities  of  hydrochloric  and  nitric 
acids  is  evidently  independent  of  the  nature  of  the  base, 
whereas  in  the  case  of  sulphuric  and  hydrochloric,  or  sulphuric 
and  nitric  acids,  the  ratio  varies  in  accordance  with  the  nature 
of  the  base.  The  reason  for  this  apparent  difference  is  to  be 
sought  for  in  the  numbers  which  express  the  volume-changes 
attending  the  action  of  sulphuric  acid  on  neutral  sulphates. 
Ostwald  shews  that  when  sulphuric  acid  and  neutral  sulphates 
react  in  equivalent  quantities,  only  a  portion  of  the  sulphate 
is  changed  into  the  acid  salt,  and  that  the  amount  of  this 
change  depends  on  the  base  present  in  the  neutral  sulphate. 
Hence,  Ostwald  concludes,  that  'sulphuric  acid. ..does  not 
'  exert  affinity  on  a  base  with  its  whole  mass  but  only  with 
'  that  part  which  is  not  combined  to  form  acid  sulphate.  The 
'greater  this  part,  the  smaller  will  the  affinity  of  sulphuric 
acid  appear  to  be.'  It  is  probable  that  the  true  relative 
affinity  of  sulphuric  acid,  like  that  of  hydrochloric  and  nitric 
acids,  is  independent  of  the  nature  of  the  base  with  which  the 
acid  combines. 


422  CHEMICAL   KINETICS.  [§§216,217 

2 1 6.  The  influence  of  temperature  on  the  relative  affinities 
of  the  three  pairs  of  acids  is  then  examined  by  Ostwald  in  the 
same  way  as  has  been  employed  for  examining  the  influence 
of  the  nature  of  the  base. 

The  results  are  contained  in  the  following  table. 


Temp. 


RELATIVE  AFFINITIES  (for  Soda). 

H9CL 


T      H2N206 
H2S04  ' 

n      H.C1, 
H2S04* 

0-61515 
—  —  =  1-90 
o-345 

o|H=I'93 

0-667 

o  *r*\/*\ 

0-6  57 
—  -  =  1-92 
o-343 

—  Z  OU 

0-333 

0-669 
^33  1  ~ 

0-666 

=  rgg 
0-334 

°703_ 
0-297 

0-703 
-^—^  =  2-37 
0-297            J/ 

H2N2O6' 
r9o~102 


s,  w/ w  ":>/_,.«„  r92 

«W 


40  '  =  2*02 =i'99  -^^=o-c 

~"""T  0-334  2'02 

-         ^      -  """      -  ,37 

Here  again  the  relative  affinities  of  hydrochloric  and  nitric 
acids  remain  constant,  while  that  of  sulphuric  acid  varies  with 
variations  of  temperature.  The  variation  in  the  value  of  the 
relative  affinity  of  sulphuric  acid  is  shewn  to  be  inversely  as 
the  amount  of  combination  of  the  acid  with  the  neutral 
sulphate ;  this  confirms  the  provisional  conclusion  that  the 
true  relative  affinity  of  sulphuric'  acid  is  in  all  respects 
comparable  with  the  relative  affinities  of  hydrochloric  and 
nitric  acids. 

The  final  result  of  the  experiments  detailed  in  Ostwald's 
first  paper  is,  that,  the  relative  affinities  of  the  acids  are  ex- 
pressed by  constant  numbers. 

217.  In  his  second  paper1,  Ostwald  extends  the  volumetric 
method  to  a  number  of  acids,  both  monobasic  and  dibasic,  in- 
cluding several  carbon-acids.  He  has  also,  in  this  paper, 
determined  the  refractive  indices  of  many  of  the  solutions  of 
acids,  bases,  and  salts  already  employed,  and  from  these  he 
has  arrived  at  measurements  of  the  amounts  of  change;  so 
that  most  of  the  data  on  which  his  calculations  are  based 

1  loc.  cit.  18.  328. 


§218]  AFFINITY.  423 

have  been  gained  by  two  independent  methods.  The  results 
agree  very  well ;  Ostwald,  however,  thinks  that  the  volumetric 
method  gives  more  trustworthy  results  than  the  optical 
method.  The  following  table  presents  the  results  of  the 
volumetric  experiments,  with  monobasic  acids,  contained  in 
Ostwald's  second  paper. 

PROPORTIONS  IN  WHICH  BASES  ARE  SHARED  AMONG  MONOBASIC 

ACIDS. 

Acids.  Potash.  Soda.          Ammonia.        Mean. 

1  Dichloracetic :  nitric  77  77  75  7& 

2  Dichloracetic  :  hydrochloric  74  75  73  74 

3  Dichloracetic :  trichloracetic  70,73  7I>71  7°>  72  71 

4  Dichloracetic :  lactic  8  9  1 1  9 

5  Monochloracetic  :  trichloracetic        92  92  92  92 

6  Formic  :  trichloracetic  97  96  97  97 

7  Formic :  lactic  43  46  48  46 

8  Formic:  acetic  25  23  23  24 

9  Formic :  butyric  21  21  19  20 

10  Formic :  isobutyric  19  19  18  19 

11  Butyric:  acetic  54  52  53  53 

12  Isobutyric  :  acetic  56  51  53  53 

1 3  Propionic :  formic  78  80  79  79 

14  Glycollic:  formic  43  44  45  44 

One  equivalent  of  the  neutral  salt  (of  potassium,  sodium, 
or  ammonium)  of  the  acid  placed  first  in  column  I.  is  acted 
on  by  one  equivalent  of  the  acid  placed  after  it  in  the  same 
column  ;  the  numbers  in  the  columns  of  bases  represent  the 
percentage  amounts  of  base  withdrawn  from  the  first  acid  by 
the  action  of  the  second. 

218.  Ostwald's  former  investigation  shewed  that  the 
relative  affinities  of  nitric  and  hydrochloric  acid  are  nearly 
identical,  the  latter  being  rather  smaller  than  the  former1. 
If  the  relative  affinity  of  nitric  acid  is  taken  as  100,  that 
of  hydrochloric  acid  is  expressed  by  the  number  98.  The 
relative  affinity  of  dichloracetic  acid  may  be  calculated  in 
terms  of  either  nitric  or  hydrochloric  acid.  Thus, 

1  This  is  confirmed  by  Thomsen's  thermochemical  work.    Fogg.  Ann.  138.  65. 


424  CHEMICAL  KINETICS.  [§  2I9 

(1)  Nitric  acid  =100;  dichloracetic  acid  =  -^x  100  =  32. 

(2)  Hydrochloric  acid  =  98;  dichloracetic  acid=  —  X98=34. 

From   this,    the   relative   affinities  of    trichloracetic    and 
lactic  acids  were  found.  .   Thus, 


Trichloracetic  acid  =      x  33  =  80. 
Lactic  acid  =^  x  33  =  3-3. 

Then  taking  trichloracetic  acid  as  80,  we  determine  the 
relative  affinities  of  monochloracetic  and  formic  acids.  Thus, 

o 

Monochloracetic  acid=—  x  80=7. 
Formic  acid  =  —  x  80=  2-5. 

But  if  we  start  with  lactic  acid  as  3*3,  and  calculate  the 
relative  affinity  of  formic  acid,  we  get  —?  x  3*3  =  3^9,  a  number 

very  much  larger  than  that  obtained  from  former  data. 
Similarly,  the  numbers  obtained  for  the  relative  affinities  of 
butyric  and  isobutyric  acids  shew  considerable  differences. 

The  numbers  obtained  for  the  relative  affinities  of  most 
of  the  acids  examined  by  Ostwald  in  this  research  cannot  be 
regarded  as  final  ;  the  method  whereby  these  numbers  are 
obtained  is  however  shewn  to  be  satisfactory  ;  and  the  deter- 
mination of  the  relative  affinities  of  acids  in  terms  of  some  one 
taken  as  unity  is  exhibited  as  a  legitimate  object  of  research. 

219.  In  his  later  investigations  Ostwald  attempts  to  use 
chemical  methods  in  attacking  the  problem  of  the  relative 
affinities  of  acids. 

When  one  substance  in  solution  reacts  on  another  in  the 
solid  state,  so  that  there  is  always  an  excess  of  the  latter 
present,  the  active  mass  of  the  solid  remains  constant1.  The 
equation  already  given  (par.  212)  viz. 


becomes  &(P-x)c=(P  + 

1  See  Guldberg  and  Waage,  J.  fur  prakt.  Chemie  (2)  19.  88. 


§  220]  AFFINITY.  425 

where  c  remains  unchanged,  as  it  expresses  the  constant 
active  mass  of  the  solid  substance. 

Suppose  it  is  desired  to  find  the  relative  affinity  of  an  acid 
by  this  method  ;  the  acid  is  allowed  to  react  on  the  insoluble 
salt  of  another  acid,  with  the  base  of  which  salt  the  given 
acid  forms  a  soluble  compound.  Let  P  represent  the  acid,  Q 
the  insoluble  salt,  P'  the  acid  of  this  salt,  and  Q  the  soluble 
salt  produced  in  the  reaction.  At  the  beginning  of  the  action 
P'  —  Q  =  o.  The  active  mass  of  Q  =  c,  and  the  only  other 
independent  variable,  P,  can  be  taken  as  equal  to  I. 

Then  the  equation  given  above  becomes 

x}c=x*',  hence  k=   .    * 


If  experiments  are  conducted  with  different  acids  and  the 
same  insoluble  salt,  various  affinity-coefficients  are  obtained  of 
the  form 

X,  X* 

&!=-,  -  *=   ,      k<t=    ,          Z=,       &C. 
^(l-Jl)  '      Jc(l-X^ 

k,     x,*l\-x     k»     x^^\-x 
Hence  -~  =  —    ,.         >  ~r  =  —    ,          • 

k      x  VI-JT,    k      ^  ^1-^2 

The  unknown  quantity  c  has  disappeared,  and  the  quo- 

k      k 
tients  -,1  ,   -y2...  represent  the  relative  affinities    of  the   dif- 

ferent acids  in  terms  of  the  first  \ 

220.  The  reactions  actually  studied  by  Ostwald  were 
(i)  that  which  occurs  when  an  acid  acts  on  solid  zinc  sulphide, 
producing  sulphuretted  hydrogen  and  a  soluble  zinc  salt  ; 
and  (2)  the  action  of  acids  on  solid  calcium  oxalate  and  zinc 
oxalate,  whereby  oxalic  acid  and  a  soluble  calcium  (or  zinc)  salt 
are  formed. 

The  first  reaction  was  however  abandoned  because  of  the 
impossibility  of  obtaining  physically  homogeneous  zinc  sul- 
phide2. 

The  second  reaction  was  found  to  be  also  open  to  objec- 
tions. Small  changes  in  the  physical  state  of  the  oxalate 

1  Ostwald,  loc.  cit.  (2)  19.  473  —  474. 

2  For  details  see  Ostwald,  loc.  cit.  (2)  19.  475  —  479. 


426  CHEMICAL  KINETICS.  [§  22O 

used   were    accompanied    by    marked    irregularities    in    the 
chemical  change.     What  Ostwald  calls  the  stability  of  the 
calcium  (or  zinc)  oxalate  conditions  the  quantity  of  this  salt 
dissolved  by  an  acid  in  a  given  time.     The  stability  is  itself 
dependent  on  the  preparation  of  the  salt,  more  especially  on 
the  amount  of  water  it  contains,  and  on  the  degree  of  dilution 
of  the  acid  employed.    Another  circumstance  tending  to  alter 
the  stability  is  the  presence,  or  absence,  of  the  neutral  alkaline 
(or  magnesium)  salt  of  the  acid  used  in  the  reaction.     Mono- 
basic acids  exert  a  greater  solvent  action,  in  a  given  time,  in 
presence  of  their  neutral  salts  than   when   those   salts   are 
absent ;  the  solvent  action  of  polybasic  acids,  on  the  other 
hand,  is  diminished  by  the  presence  of  their  neutral  salts. 
This  subject  is  worked  out  in   detail  by  Ostwald,  and  it  is 
shewn  that  the  neutral  salt  probably  acts  on  the  calcium  (or 
zinc)  oxalate  to  a  very  small  extent  and  decomposes  a  little 
of  it,  and  that  the  solvent  action  of  the  acid  is  increased  by 
this  change  in  the  stability  of  the  oxalate  *.     Developing  this 
hypothesis,  and  applying  the  theory  of  Guldberg  and  Waage, 
Ostwald  arrives  at  the  result,  that  the  modifying  influence  on 
the  chemical  equilibrium  of  a  system,  exerted  by  the  stability 
of  a  solid  member  of  that  system,  is  of  the  same  nature  as  the 
influence  exerted  by  the  affinities  of  the  reacting  substances  *. 
As  regards  the  modifying  influence  of  dilution  it  is  shewn 
that  the  amount  of  calcium  (or  zinc)  oxalate  dissolved  in- 
creases, up  to  a  certain  limit,  as  the  quantity  of  water  present 
increases.     The  action  of  water  is  probably  twofold;  (i)  it 
forms  more  or  less  stable  compounds  with  the  acid,  and  thus 
reduces   the   solvent   action   of  the   latter;    (2)    it   exerts   a 
decomposing  action  on  the  oxalate,  and  thus  increases  the 
solvent  action  of  the  acid.     In  the  cases  studied,  the  latter 
action  preponderated 3. 

As  a  general  result  of  this  part  of  his  research,  Ostwald 
concludes,  that   the  action    of  the  acids  on  insoluble   salts 

1  Ostwald,  loc.  cit.  (2)  23.  218 — 222. 

2  Do.  do.  (2)  23.  222—226. 

3  Do.  do.  (2)  23.  527—528;  and  do.  (2)  22.  305  et  seq.     See  also  ante,  chap. 
H.  par.  181. 


§§221,  222]  AFFINITY.  427 

presents  a  suitable  means  for  determining  the  relative  affini- 
ties of  these  acids,  provided  the  solutions  of  the  acids  employ- 
ed are  as  dilute  as  possible  \ 

221.  The  methods  thus  far  employed  by  Ostwald  have 
been  based   on   the   study   of  the   equilibrium   of  chemical 
systems  wherein  two  equal  and  opposite  processes  of  change 
are  proceeding.     But,  as  we  saw  in  par.  205,  the  theory  of 
Guldberg  and  Waage  may  also  be  applied  to  determine  the 
values  of  coefficients  of  affinity  from  measurements  of  the 
velocities    of  chemical    operations.      Guldberg    and    Waage 
themselves  tested  their  theory  by  applying  it  in  this  way. 
The  chemical  change,  whose  velocity  is  to  be  observed,  must 
be  a  simple  process,  otherwise  the  difficulties  of  calculation 
become  at  present   insurmountable,  but   it  must  also  be  a 
representative  process,  otherwise  the  results  are  not  capable 
of  wide  application  *. 

Ostwald  therefore  determined  to  measure  the  velocities  of 
some  of  those  processes  the  relative  affinities  of  the  substances 
taking  part  in  which  had  already  been  roughly  determined  by 
equilibrium-methods. 

He  would  thus  find  values  for  these  affinities  by  two 
different  applications  of  the  theory  of  Guldberg  and  Waage. 

222.  The  operation  formulated  as 

R.CO.NH2  +  HOH  =  R.COO.NH4 

occurs  in  the  presence  of  acids ;  the  velocity  of  the  change 
depends  on  the  dilution  of  the  acid  employed,  the  tempera- 
ture, and  the  nature  of  the  acid  which  exerts  a  'predis- 
posing affinity'  (see  ante,  chap.  II.  par.  179)  on  the  reac- 
tion. The  process  proceeds  evenly,  and  the  velocity  is 
easily  determined  by  measuring  the  amount  of  ammonium 
salt  produced,  by  decomposition  with  sodium  hypobromite3. 

1  loc.  cit.  (2)  23.  536. 

2  The  results  obtained  by  Menschutkin,  Kajander,  and  others,  as  also  those 
detailed  in  Guldberg  and  Waage's  Ettides,  are  not  suitable  for  deducing  the  values 
of  coefficients  of  affinity.     (See  Ostwald,  loc.  cit.  (2)  27.  i.) 

3  Ostwald,  loc.  cit.  (2)  27.   i.     Many  preliminary  trials  were  made,  and  the 
value  of  a  small  correction  for  the  nitrogen  evolved  by  the  amide  present  was 
determined  :  for  a  description  of  the  methods  of  procedure  see  pp.  5 — 14. 


428  CHEMICAL   KINETICS.  [§  222 

Acetamide  was  employed  ;  the  experiments  were  made  at 
65°  and  1 00°,  for  intervals  of  time  varying  from  2  minutes  to 
50  days. 

The  amounts  of  chemical  change,  for  given  intervals 
of  time,  at  a  constant  temperature,  are  determined  and 
tabulated  for  each  acid  employed;  then,  by  the  use  of  an 
interpolation-formula,  the  time  is  found  which  is  required  by 
each  acid  to  accomplish  50  per  cent,  of  the  total  change ;  and 
lastly,  by  dividing  the  intervals  of  time  in  the  first  table  by 
the  times  required  for  the  half-completion  of  the  process, 
comparable  numbers  are  obtained  which  express  the  amount 
of  change  effected  by  each  acid  in  the  same  time.  Putting 
the  velocity  as  inversely  proportional  to  the  time  required 
for  reaching  a  determinate  stage  of  the  decomposition,  it 
is  shewn  that  the  ratios  of  the  velocities  of  different  acids 
are  not  constant,  but  depend  on  the  stage  of  the  operation 
selected. 

Ostwald,  as  we  have  seen,  selects  the  stage  at  which  the 
operation  is  half  completed ;  the  velocities  are  stated  in  terms 
of  that  of  hydrochloric  acid  taken  as  100. 

RELATIVE  VELOCITIES. 

65°  100° 

Hydrochloric       acid  100  100 

Nitric                      „  98  97 

Hydrobromic         „  98  98 

Trichloracetic        „  80 

Dichloracetic         „  40*8 

Monochloracetic    „  13*0 

Formic                    „  5'i  4'^3 

Lactic                     „  5-13  4-85 

Acetic                     „  2-34 

Sulphuric                „  65-4  59*4 

Oxalic                      „  22'6  20'5 

Tartaric                  „  7'S1  7'32 

Malic                      „  4^67 

Succinic                 „  2*55  2*5 

Citric                      „  4'oi  4'oi 

Phosphoric             „  3*58 

Arsenic                   „  3'53 


§  223]  AFFINITY.  429 

A   curve  theoretically  representing   the   progress  of  the 

change  is  constructed  by  help  of  the  formula  =  Ct, 

where  y  —  amount  of  acid  decomposed  in  time  /,  the  active 
mass  of  which  acid  at  the  beginning  of  the  reaction  is  repre- 
sented by  a,  and  C=  a  constant. 

This  equation  is  obtained  by  developing  the  fundamental 
equation  given  by  Guldberg  and  Waage1,  v=(f>(T—T'}}  it 
therefore  assumes  the  correctness  of  the  law  of  mass-action 
formulated  by  these  naturalists,  and  also  that  the  substances 
formed  during  the  reaction  exert  no  influence  on  the  process. 
The  actually  observed  results  are  plotted  alongside  the 
theoretical  curve ;  the  curves  representing  the  process  at  65° 
and  1 00°  are  nearly  identical. 

A  comparison  of  the  curve  calculated  by  the  formula,  with 
the  results  plotted  alongside,  shews  that  the  process  is  not 
entirely  free  from  secondary  reactions.  Among  these  se- 
condary reactions  are  to  be  placed  the  influence  of  the  neutral 
ammonium  salts  of  the  monobasic  acids  (see  ante,  par.  220), 
the  influence  of  the  acid  ammonium  salts  of  the  polybasic 
acids,  and  the  probable  formation  of  amido-acids  in  the  case 
of  trichloracetic  acid,  &c.  Nevertheless,  the  numbers  ob- 
tained are  comparable  with  those  arrived  at  by  Ostwald's 
former  equilibrium-studies,  inasmuch  as  the  secondary  changes 
in  both  series  of  reactions  are  very  similar2. 

223.  In  a  former  paper  it  had  been  shewn  by  Ostwald, 
that  when  equilibrium  is  established  by  the  competition  of 
two  acids  for  the  same  base,  the  factors  k  and  k'  in  Guld- 
berg and  Waage's  fundamental  equation,  may  with  great 
probability  be  resolved  each  into  two  parts,  one  dependent 
on  the  nature  of  the  base,  and  the  other  on  the  nature  of  the 
acids 3.  Treating  k  and  k'  in  this  way,  he  gets 

,          a.  .5  ,    .,        a'.  3 

k=c~~   ,  and  k'  =  c — £; 
a  .  p  a.  p 

where  a  and  a'  depend  on  the  nature  of  the  acids,  and  ft  on 

1  For  details  see  Ostwald,  loc.  cit.  (2)  27.  24  and  31. 

2  For  further  discussion  see  Ostwald,  loc.  cit.  (2)  27.  24 — 31. 

3  loc.  cit.  (2)  16.  422.     See  also /to/,  par.  227. 


430  CHEMICAL   KINETICS.  [§  224 

that  of  the  base,  c  being  a  constant.     Hence  T>  =  -75 ;  and  as 

K          CL 

a  and  a'  depend  (probably)  only  on  the  nature  of  the  acids, 
and  measure  their  affinities,  it  follows  that  the  values  of  these 
affinities  are  as  the  square  roots  of  the  velocities  of  the 
reactions  wherein  the  acids  take  part  *. 

The  relative  affinities  of  the  various  acids  employed  in 
this  investigation  are  then  calculated  from  the  observed 
velocities,  that  of  hydrochloric  acid  being  taken  as  100.  The 
results  agree  very  fairly  with  those  formerly  obtained  (see 
post,  par.  235).  It  is  to  be  remembered  that  both  series  of 
numbers  are  affected  by  the  occurrence  of  secondary  changes 
in  the  chemical  operations  from  the  study  of  which  they  were 
deduced. 

We  have  already  learned  (ante,  chap.  II.  par.  187)  that 
the  molecular  theory  of  chemical  action  points  to  a  close 
connection  between  the  rates  at  which  chemical  changes 
proceed,  and  the  affinities  (using  this  term  in  a  wide  sense)  of 
the  reacting  bodies.  This  connection  is  now  seen  to  be  em- 
phasised, and  rendered  exact,  by  the  more  purely  dynamical 
studies  based  on  Guldberg  and  Waage's  theory  of  affinity2. 

224.  These  studies  are  continued,  with  similar  results,  in 
Ostwald's  next  paper,  where  the  operation  represented  by  the 
equation 

CH3.  COOCH3  +  HOH  =  CH3.  COOH  +  CH3.  OH 

is  selected  for  investigation,  as  being  simple,  and  also  typical3. 
The  change  proceeds  at  different  rates  in  the  presence  of 
different  acids.  The  action  of  the  acids  belongs  to  the  class 
known  as  contact  or  catalytic  actions  (see  ante,  chap.  II. 
par.  178). 

Ostwald  has  carefully  examined  this  process,  using  various 
acids,  varying  the  time  of  action,  &c.,  and  has  convinced 
himself  that  the  operation  is  in  all  cases  of  the  same  kind, 

1  For  a  fuller  treatment  of  this  part  of  the  subject  see  Ostwald,  loc.  cit.  (2)  27. 
35—36- 

2  We  have  here  an  instance  of  the  merging  into  one,  of  the  two  paths  of 
chemical  advance. 

3  loc.  cit.  (2)  28.  449. 


g)  225,  220J  AFFINITY.  431 

and  that  the  same  formula  for  finding  the  amount  of  methylic 
acetate  decomposed  may  always  be  used,  viz. 

b  lc 

log  -.  —    =  c .  a  .  t.  or,  log  I  —  -r=c .  a .  f, 
b  —  x  o 

where  a  =  amount  of  acid,  b  —  amount  of  ethereal  salt  at  the 
beginning  of  the  reaction,  and  x  =  amount  of  this  salt  de- 
composed in  time  t,  c  being  a  constant  \ 

The  action  is  completed  and  equilibrium  established  in 
24  hours  ;  it  is  not  however  always  necessary  to  carry  the 
process  to  this  final  state,  inasmuch  as  it  can  be  shewn  (and 
this  is  verified  by  experiment)  that  the  final  state  is  reached 
after  a  period  ten  times  as  long  as  that  during  which  50  per 
cent,  of  the  ethereal  salt  is  decomposed 2. 

225.  Having  thus   satisfied   himself  as   to   the   general 
character   of  the  reaction  which  occurs  in  the  catalytic  de- 
composition of  methylic  acetate  by  acids  in  presence  of  water, 
Ostwald   proceeds   to   study  the   influence    exerted   on   the 
velocity  of  the  change  by  varying  the  acids  employed.     His 
results  are  tabulated  (pp.  472 — 486)  and  the  square  roots  of 
the  different  velocity-coefficients  are  given  in  terms  of  that  of 
hydrochloric  acid  as  100.     The  affinities  of  the  acids  as  thus 
obtained  are  represented  by  larger  numbers  than  those  ar- 
rived at  by  the  use  of  equilibrium-methods  (see  table  loc.  cit. 
p.  487  ;  2\$Q  post,  par.  235).     But  this  apparent  increase  in  the 
values  of  these  affinities  is  shewn   to  be  due  to  secondary 
actions,  between  methylic  acetate  and  water,  which  occur  in 
the   process   in   question.      Nevertheless,   the   two   series   of 
numbers  exhibit  the  closest  parallelism  even  in  small  details. 

226.  In  a  later  communication 3,  Ostwald  shews  that  the 
'  inversion  '  of  cane  sugar  in  presence  of  various  acids  follows 
the   same   course   as   the   change   of  methylic   acetate   into 
alcohol  and  acid.    He  employs  the  formula  already  given,  viz. 

log— l—  =  c.a.t,  or  log£—^=c.a.t. 
l~~b 

1  See  loc.  cit.  (2)  28.  451—472  for  details  regarding  this  formula  and  the  ways 
in  which  Ostwald  has  tested  its  validity. 

8  loc.  cit.  (2)  28.  452—453.  »  loc.  cit.  (2)  29.  385. 


432  CHEMICAL  KINETICS.  [§  22/ 

The  values  obtained  for  logT are  multiplied  by  1000 

to  avoid  fractions. 

The  quotient  obtained  by  dividing  these  values  by  the 
time  of  action  should  be  a  constant  quantity;  this  constant, 

c  —  log  T /  a.t.,  Ostwald  calls  the  inversion-  (or  velocity-) 

constant.  The  results  shew  that  the  observed  variations  in 
the  values  of  this  quantity  are  very  small,  and  are  such  as 
may  be  fairly  attributed  to  errors  of  experiment  (loc.  cit. 

p.  401). 

The  square  roots  of  the  velocity-constants  represent  the 

relative  affinities  of  the  acids  employer1.  The  numbers  ob- 
tained from  this  investigation  agree  very  closely  with  those 

deduced  from  the  experiments  with  methylic  acetate ;  see 
table,  par.  235. 

In    this    paper    Ostwald    gives    a    table    shewing  the 

values  of  log  ,_    ,  or  log  — — • ,  for  all  values  of  -j  between 

l~~b 

O'OOi  and  0*999,  to  facilitate  the  calculations  of  those  who 
may  investigate  the  velocity-constants  of  various  reactions. 

•ft 

227.  From  all  these  researches,  Ostwald*  concludes  that 
each  acid,  and  each  base,  possesses  a  specific  affinity-constant; 
and  that  all  the  chemical  reactions  in  which  the  acid,  or  base, 
plays  a  part  are  determined  by  the  magnitude  of  this  con- 
stant. The  researches  on  the  decomposition  of  acetamide, 
and  of  methylic  acetate,  by  water  in  presence  of  acidc,  have 
shewn  that  changes  wherein  'predisposing  affinity'  and 
'  catalytic  actions '  are  factors,  are  conditioned  by  the  affinity- 
constants  of  the  acids,  as  determined  by  the  application  of 
Guldberg  and  Waage's  theory.  And  the  researches  on  the 
action  of  acids  on  insoluble  salts  (see  ante,  par.  220)  have 
shewn  that  the  influence  exerted  by  the  stability  of  such  salts 
on  the  equilibrium  of  the  system  is  of  the  same  kind  as  that 
exerted  by  the  affinities  of  the  reacting  substances.  Some  of 
Ostwald's  pupils  have  recently  shewn  that  the  solvent  actions 
of  various  dilute  acids  on  cream  of  tartar,  and  on  the  sulphates 


§§  228,  229]  AFFINITY.  433 

of  barium,  strontium,  and  calcium,  obey  the  same  law  ;  each 
acid  acts  in  accordance  with  its  mass  and  its  specific  affinity- 
constant  *. 

228.  The  questions  thus  partly  solved  by  Ostwald  have 
been  attacked  by  J.  Thomsen  by  thermochemical  methods. 

When  two,  or  more,  acids  and  one  base  react  in  equiva- 
lent quantities,  in  a  dilute  aqueous  solution,  what  are  the 
proportions  in  which  the  acids  combine  with  the  base  ? 
Measurements  of  thermal  changes  must,  it  would  seem,  throw 
light  on  this  question.  The  process  evidently  is  one  wherein 
an  equilibrium  is  established.  Can  the  distribution  of  the 
masses  of  the  acting  bodies  be  deduced  from  measurements 
of  the  thermal  gains  or  losses  which  accompany  this  distribu- 
tion ? 

229.  Thomsen's   method    of   attacking    these    questions 
rests  upon  the  following  considerations. 

The  various  acids,  by  neutralisation  with  the  same  base, 
develop  unequal  quantities  of  heat.  Now  if  one  acid  re- 
places another  from  its  combination  with  a  given  base,  the 
operation  will  be  attended  by  a  thermal  change,  which  will 
be  positive  or  negative  according  as  the  free  acid,  or  the  acid 
already  combined  with  the  base,  possesses  the  greater  heat 
of  neutralisation.  The  extent  of  the  reaction  can  be  deduced 
from  measurements  of  the  thermal  values  of  the  different 
parts  of  the  operation.  Thus,  take  the  reaction  between 
nitric  acid  and  sodium  sulphate ;  the  thermal  values  of  the 
following  changes  must  be  determined. 

(1)  Neutralisation  of  sulphuric  acid  by  soda. 

(2)  Neutralisation  of  nitric  acid  by  soda. 

(3)  Decomposition  of  sodium  sulphate  by  nitric  acid. 

(4)  Decomposition  of  sodium  nitrate  by  sulphuric  acid. 

(5)  Action  of  sulphuric  acid  on  sodium  sulphate. 

(6)  Action  of  nitric  acid  on  sodium  nitrate. 

(7)  Action  of  sulphuric  acid  on  nitric  acid2.      • 

1  J.fiirprakt.  Chemie  (2)  29.  49. 

2  Thomsen,  Thertnochetnische  Untersuchungen  1.  98. 

M.  C.  28 


434  CHEMICAL   KINETICS.  [§  230 

230.  Now  when  nitric  acid  and  sodium  sulphate  react,  in 
equivalent  quantities,  in  a  dilute  aqueous  solution,  heat  is 
absorbed  ;  but  when  sulphuric  acid  and  sodium  nitrate  react, 
under  similar  conditions,  heat  is  evolved.  But  the  final  dis- 
tribution of  the  base  between  the  two  acids  will  be  the  same 
in  both  cases  ;  and  moreover  this  distribution  will  be  the 
same  as  that  which  results  when  equivalent  quantities  of  the 
two  acids  (sulphuric  and  nitric),  and  the  base  (soda)  mutually 
react. 

This  statement  may  be  put  in  a  general  form  thus.  Let 
the  three  bodies  A,  B,  and  A'  react  in  equivalent  quantities, 
in  a  dilute  aqueous  solution  ;  then, 


hence  \A'B,  A}  -  [AB,  A']=[A,  B]  -  [A',  B]. 

Now   if  A  =  SO3Aq  ;    B  =  Na2OAq  ;    and   A'  =  N2O5Aq  ;    it 
follows  that 

[Na2N2O6Aq,  SO3Aq]-  [Na2SO4Aq,  N2O5Aq]  =  [Na2OAq,  SO3Aq] 

-  [Na2OAq,  N2O5Aq]. 

The  differences  between  the  thermal  values  actually  observed 
were  4,144  and  4,080  gram-units  respectively1. 

When  an  equivalent  of  nitric  acid  (A')  reacts  on  one 
equivalent  of  sodium  sulphate  (A  B)  with  decomposition  of  x 
equivalents  of  the  latter  salt,  the  final  distribution  of  acids 
and  base  may  be  represented  by  the  expression, 

(i  -x)AB+xA'B+xA  +  (i  -x)  A'. 

And  the  total  thermal  change  accompanying  this  operation 
will  consist  of  the  following  partial  changes  ; 

(a]    that  attending  the  decomposition  of  x  equivalents  of  AB, 
i.e.  Na2SO4; 

(b}    that  .attending  the  formation  of  x  equivalents  of  A'B,  i.e. 

Na2N206  ; 

1  loc.  cit.  p.  112. 


§231]  AFFINITY.  435 

(c)  that  attending  the  reaction  of  x  equivalents  of  the  acid  A, 
i.e.  H2SO4,  on  (i  -  x]  equivalents  of  the  salt  AB  ; 

(d)  that  attending  the  reaction  of  ( I  -  x]  equivalents  of  the  acid  A', 
i.e.  HNO3,  on  x  equivalents  of  the  salt  A ' B ;  and 

(e)  that  attending  the  reaction  of  x  equivalents  of  the  acid  A  on 
(i  —x)  equivalents  of  the  acid  A'. 

The  total  thermal  change  may  therefore  be  expressed  by 
the  formula, 

[AB,  A']  =  x[(A',  B}-( 


231.  Values  have  been  found  by  Thomsen  for  all  the 
partial  thermal  changes,  except  the  last,  the  value  of  which 
is  so  small  that  it  cannot  be  accurately  determined,  and  may 
therefore  be  omitted  from  the  calculation. 

The  following  data,  required  for  determining  the  values  of 
the  reactions  (a),  (b),  (c),  are  the  results  of  a  large  series  of 
measurements  made  by  Thomsen  2. 

DATA  FOR  REACTION  (a). 

(1)  [Na'OAq,  SO3Aq]=3i,378. 

(2)  n-  [Na2S04Aq,  ;;N2O5Aq] 

k  ~  9°4 

J  -1616 

i  -2584 

i  -  3504 

'   2  -4052 

3  -4100. 

The  complete  decomposition  of  Na2SO4  into  Na2N2O6  is 
attended  with  the  absorption  of  4144  gram-units  of  heat 

(3)  y  [Na2S04.^S03Aq,  2N205Aq] 

0  -  4052 

1  -1956 

2  -1328 

3  - 1040. 

1  loc.  cit.  p.  113.  *  loc.  cit.  pp.  99—110. 

28—2 


436  CHEMICAL  KINETICS.  [§  232 

(4)  /3  [iNa2SO4  .  ^Na2N2O6Aq,  /3N2O5Aq] 


1  -  1092 

£  -1522 

i  -  1936. 

DATA  FOR  REACTION  (b). 

(1)  [Na2OAq,  N2O5Aq]  =  27,234. 

(2)  [Na2N206Aq,  N2O5Aq]=  -78  (as  this  is  so  small  it  is  neglected 
in  the  calculations). 

(3)  «  [Na2N206Aq,  ;/SO3Aq] 

1  576 

2  758. 

DATA  FOR  REACTION  (c). 
n  [Na2SO4Aq,  «SO3Aq] 

•  i  -792 

i  -1262 

1  -1870 

2  -2352 

4  -  2682. 

The  following  approximate  formula  is  deduced  for 
finding  the  thermal  value  of  this  reaction  for  any  value 
of  n: 

[Na2S04Aq,  « 


232.  Substituting  the  chemical  formulae  of  the  various 
bodies,  and  the  actually  observed  thermal  values,  in  the 
equation  in  par.  230,  p.  435,  we  have  this  result: 

[Na2SO4Aq,  N2O5Aq]=^r[N2O5Aq,  Na2OAq]  -[SO3Aq,  Na2OAq] 

+  (i-.r)[Na2S04Aq,  y^SO3Aq] 
(the  thermal  values  of  the  other  parts  are  so  small  that  they  are  omitted) 

=  -x.  4i44  +  (i  -*•)  [Na2S04Aq,  j^.SO3Aq] 
=  -3504. 

Then,  from  the  actually  observed  thermal  values  of  the 
reaction  between  Na2SO4Aq,  and  ;zSO3Aq  (see  data  for 
reaction  (c)),  a  value  must  be  sought  for  x  which  shall  give  a 
result  in  agreement  with  the  total  thermal  value  of  the 


§§  233,  234]  AFFINITY.  437 

change,  which  value  is  -3504.  If  x  is  taken  as  equal  to  f, 
we  get  this  result : 

[Na2SO4Aq,  N2O5Aq]=  -  |.  4M4  +  KNa2SO4Aq,  2SO3Aq] 
=  -1.4144-1.2352 

=  -  3547- 

The  difference  between  the  observed  and  calculated  values  is 
only  about  1*25  per  million  of  the  heat  of  neutralisation. 
The  thermal  value  of  the  reverse  action,  that  namely  between 
sulphuric  acid  and  sodium  nitrate,  is  found  by  the  equation, 

[Na2N206Aq,  SO3Aq]  =  (i  -*)4i44+(i  -;tr)[Na2SO4Aq,^.  SO3Aq] 
=  598. 

The  observed  value  was  576  ;  the  difference  does  not  amount 
to  more  than  "/  per  million  of  the  heat  of  neutralisation. 

233.  From   these  results,  Thomsen  draws  the  following 
conclusions. 

(a)  When  soda,  nitric  acid,  and  sulphuric  acid  mutually 
reapt<v  in  equivalent  quantities,  in  a  dilute  aqueous   solution, 
two-thirds  of  the  soda  combines  with  the  nitric  acid,  and 
one-third  with  the  sulphuric  acid. 

(b)  The  final  division  of  the  base   between   the   two 
acids  is  the  same  whether  the  soda  were  originally  present  as 
sulphate  or  nitrate1. 

(c)  The   striving   of  the   nitric  acid  to  saturate  itself 
with  the  base  •(//#.$•  Bestreben  sick  mit  der  Basis  zu  sdttigen\ 
is  twice  as  great  as  that  of  the  sulphuric  acid.     Nitric  acid,  in 
aqueous  solution,  is  therefore  a  stronger  acid  than  sulphuric 2. 

This  striving  of  the  acids  towards  neutralisation.  Thomsen 
calls  the  avidity  of  the  acids.  The  expression  evidently 
conveys  exactly  the  same  meaning  as  the  term  affinity  in 
Ostwald's  nomenclature. 

234.  Applying  the  method  sketched  above  to  the  case  of 
hydrochloric  and  sulphuric  acids  reacting  on  soda,  Thomsen 
gets  the  following  result : 

[Na2OAq,  H2Cl2Aq]  =  27,480. 

1  The  truth  of  this  statement  has  already  been  assumed  (par.  230). 

2  loc.  fit.  p.  114. 


CHEMICAL  KINETICS.  [§235 

Let      ^  =  SO3Aq;  ^=Na2OAq,  and  yf  =  H2Cl2Aq;  and  let  x=%. 
See  equation  par.  230. 

Then         [Na2SO4Aq,  H*Cl2Aq]=  -§.  3898 -J.  2352=  -  3383  : 

observed,  -3364. 

And        [Na2Cl2Aq,  SO3Aq]=  +-J.  3898-  \  .  2352  =  515  :  observed,  488. 

The  differences  between  the  observed  and  calculated 
numbers  amount  to  less  than  I  per  million  of  the  heat  of 
neutralisation. 

Hence,  the  avidity  (affinity)  of  hydrochloric  acid  for  soda 
is  equal  to  that  of  nitric  acid,  and  is  twice  as  great  as  that  of 
sulphuric  acid  for  the  same  base  *. 

Thomsen  has  determined  the  relative  avidities  (affinities) 
of  many  acids  by  this  thermochemical  method ;  his  results 
are  given  in  the  table  on  p.  441. 

Thomsen  then  applies  the  theory  of  Guldberg  and  Waage 
to  his  results2,  and  shews  that  the  numbers  obtained  by 
experiment  agree  very  well  with  those  calculated  by  the  use 
of  equations  deduced  from  this  theory. 

235.  The  following  table  contains  Ostwald's  results  re- 
garding the  relative  affinities  of  acids. 

The  numbers  in  column  I  are  those  obtained  by  the  study 
of  the  inversion  of  sugar  by  various  acids. 

The  numbers  in  column  II  are  those  obtained  by  the 
study  of  the  decomposition  of  methylic  acetate  by  water  in 
presence  of  acids. 

The  numbers  in  column  in  are  those  obtained  by  the 
study  of  the  decomposition  of  acetamide  by  water  in  presence 
of  acids. 

The  numbers  in  column  IV  are  those  obtained  by  measur- 
ing the  volume-changes  which  occur  when  various  acids  and 
bases  are  mixed  in  equivalent  quantities. 

The  numbers  in  columns  v  and  VI  are  those  obtained  by 
studying  the  action  of  dilute  acids  on  calcium  oxalate3;  those 

1  loc.  cit.  p.  115. 

2  loc.  cit.  pp.  118 — 124. 

3  The  details  of  the  investigation  from  which  these  numbers  are  obtained  have 
not  yet  been  published  ;  the  work  has  been  conducted  by  one  of  Ostwald's  pupils. 


!35]  AFFINITY. 

RELATIVE  AFFINITIES  OF  ACIDS.    (OSTWALD.) 


439 


ACID 

I 

sugar 
inversion 

ii 

methyl 
acetate 

in 

acetamide 

IV 

division  of 
base 
between 
2  acids 

V 
acids  on 
normal 

VI 

CaC204; 
i  -ioth  nrml. 

Hydrochloric 

100 

100 

100 

98 

100 

97-9 

Hydrobromic 

I05-5 

99'I 

98 

— 

94*9 

99 

Hydriodic 

98-I 

—  . 

Nitric 

100 

957 

98 

100 

no 

100 

Chloric 

101-8 

97  -2 



103-6 

99'8 

Sulphuric 

73-2 

73"93 

65-4 

66 

70 

74*2 

1[io4-56] 

Methyl  sulphuric 

— 

100-37 

— 

— 

— 

— 

Ethyl  sulphuric 

100 

99-33 

— 

— 

— 

— 

Propyl  sulphuric 

— 

98-98 

_ 

— 

— 

— 

Isobutyl  sulphuric 

— 

98-53 



— 

— 

— 

Amyl  sulphuric 

— 

97-82 

— 

— 

— 

— 

Ethyl  sulphuric 

95'4 

98-94 

— 

— 

— 

— 

Tsethionic 

95  "9 

98-87 

— 

— 

— 

— 

Benzene  sulphonic 

I02'2 

99'54 

— 

— 

— 

— 

Formic 

I2'4 

11-49 

5 

3'9 

2-59 

12-9 

Acetic 

6-32 

5-87 

2'34 

1-23 

1-05 

7'35 

Propionic 

5'5i 

1*04 

Butyric 

— 

5  '47 

— 

0-98 

— 

—  - 

Isobutyric 

579 

5-18 

— 

0-92 

— 

— 

Monochloracetic 

22 

20-8 

13 

7 

5-1 

21-3 

Dichloracetic 

52-1 

48 

40-8 

33 

18-3 

48-8 

Trichloracetic 

86-8 

82-6 

80 

80 

64-2 

89-9 

Glycollic 

11-4 

— 

.  — 

— 

— 

Diglycollic 

16-3 

— 

— 

— 

— 

— 

Lactic 

10-3 

9-49 

5 

3'3 

4'i 

I3'3 

Methoxyacetic 

I3-5 

— 

Ethoxyacetic 

117 

— 

—            — 

— 

'  — 

Methoxypropionic 

11-8 

— 

— 

— 

— 

— 

Hydroxyisobutyric 

10-3 

9  -60 

— 

— 

— 

— 

Trichlorolactic 

26-3 

—            — 

— 

— 

Pyruvic 

25-5 

25-9 

—            — 

— 

— 

Oxalic 

43 

43 

22-6 

— 

— 

— 

Malonic 

17-5 

16-9 



—             — 

— 

Glyceric 

1  3*1 

— 



—             — 

— 

Succinic 

7-38 

7-04 

2'5 

i  '45 

2-05 

9*3 

Malic 

11-3 

10-86 

4'7 

2-82 

5-05 

12-05 

Tartaric 

15-15 

7'5 

5  "2 

(?)  4-62 

14*16 

Pyrotartaric 

10-3 

— 

Racemic 

JS'^ 

— 

— 

— 

— 

Citric 

13-1 

1279 

4 

— 

3-o6 

14-44 

Phosphoric 

24-9 

— 

Arsenic 

21-9 

— 

— 

— 

— 

— 

1  The  affinity  of  sulphuric  acid  appears  less  than  that  of  its  derivatives  obtained 
by  replacing  hydrogen  by  indifferent,  or  even  basic,  radicles.  But  it  is  to  be  noted 
that  £  H2SO4  is  compared  with  SO2 .  OH .  OCH3  &c.  If  molecular  quantities  are 


44°  CHEMICAL  KINETICS.  [§  235 

in  V  represent  the  results  of  the  use  of  normal  solutions,  and 
those  in  VI  of  T^th  normal  solutions  of  acids. 

The  numbers  in  column  I  are  regarded  by  Ostwald  as 
the  most  trustworthy ;  the  reaction  employed  is  freer  from 
secondary  actions  than  any  of  the  others.  The  numbers  in 
column  II  are  also  very  satisfactory ;  the  reaction  used 
(CH3. COO. CH3+HOH  =  CH3.COOH+CH3.OH)was  simpler 
than  any  of  those  by  which  the  numbers  in  the  succeeding 
columns  were  obtained ;  the  acids  whose  affinity-constants  were 
sought  for  remained  in  the  free  state  throughout  the  whole 
process,  so  that  no  complication  could  arise  from  the  for- 
mation of  acid  salts,  &c.  such  as  occurred  in  the  processes 
investigated  in  columns  III  to  VI.  There  was  only  one 
secondary  action,  namely,  that  due  to  the  presence  of  free 
acetic  acid,  and  the  influence  of  this  could  be  partially  elimi- 
nated in  the  calculations. 

The  two  series  of  numbers  obtained  by  employing  the 
reaction  of  acids  on  solid  calcium  oxalate  differ  greatly,  but 
the  arrangement  of  the  acids  in  accordance  with  their  affinities 
is  the  same  in  both.  The  numbers  obtained  by  using  dilute 
acids  (-j^th  normal),  column  VI,  agree  very  well  with  those  in 
column  II,  while  the  numbers  deduced  from  observations  with 
stronger  solutions  (normal),  column  V,  agree  better  with 
those  based  on  measurements  of  volume-changes,  column  IV ; 
hence,  Ostwald  argues,  the  explanation  before  given  regarding 
the  combined  action  of  water  and  acid  on  calcium  oxalate  is 
confirmed.  When  very  dilute  solutions  of  acids  are  employed, 
the  water  exerts  an  action  on  the  solid  salt  independently  of 
the  acid,  just  as  in  the  reaction  from  which  the  numbers  in 
column  II  are  obtained  there  is  a  twofold  action,  partly  due 
to  the  water  and  partly  to  the  acid.  It  will  still  be  necessary 
to  endeavour  to  separate  these  actions  before  numbers  are 
obtained  which  represent  the  affinity-constants  of  the  acids 
alone.  From  experiments  not  yet  published,  Ostwald  thinks 
that  the  numbers  obtained  by  studying  the  division  of  bases 
between  two  acids  are  affected  by  a  source  of  error  which 

to  be  compared,  the  observed  numbers  for  sulphuric  acid  reactions  must  be 
doubled  ;  if  this  is  done  the  affinity  of  this  acid  is  104*56. 


§  236]  AFFINITY.  441 

makes   the   stronger  acids  appear  stronger,  and  the  weaker 
acids  weaker,  than  they  really  are  (loc.  cit.  (2)  29.  403). 

The  results  obtained  by  therrnochemical  methods  are 
presented  in  the  following  table. 

RELATIVE  AFFINITIES  (avidities)  OF  ACIDS.    (THOMSEN1.) 

ACID.  ACID. 

Nitric  100  Oxalic  24 

Hydrochloric  100  Orthophosphoric  13 

Hydrobromic  89  Monochloracetic  9 

Hydriodic  79  Hydrofluoric  5 

Sulphuric  49  Tartaric  5 

Selenic  45  Citric  5 

Trichloracetic  36  Acetic  3 

236.  We  have  already  seen  that  from  his  volumetric 
experiments  on  the  division  of  a  base  between  two  acids, 
Ostwald  concluded  that  the  true  relative  affinities  of  hydro- 
chloric, nitric,  and  sulphuric  acids  are  independent  of  the 
nature  of  the  base  (see  ante,  par.  223).  If  this  holds  good  for 
all  acids,  the  conclusion  is  arrived  at  that  the  relative  affinities 
of  bases  are  independent  of  the  nature  of  the  acids  on  which 
they  react. 

Stating  the  absolute  affinity  of  an  acid  A,  for  a  base,  C,  in 
the  form/"  (A,  C\  the  statement  just  made  may  be  put  thus 


that  is,  the  affinity  between  an  acid  and  a  base  is  the  product 
of  the  specific  affinity-constant  of  the  acid,  and  the  specific 
affinity-constant  of  the  base  2. 

This  conclusion  is  confirmed,  on  the  whole,  by  Thomsen's 
therrnochemical  researches.  It  was  mentioned  in  pars.  222  —  3 
that  Ostwald  had  developed  Guldberg  and  Waage's  funda- 
mental equation  for  finding  the  velocity  of  a  chemical  change, 

1  loc-  cit.  1.  308.     The  numbers  given  by  Thomsen  are  calculated  for  equiva- 
lent weights  of  the  various  acids  (e.g.  for  HC1,  |H2SO4,  ^H3.C6H5O7,  &c.), 
except  in  the  case  of  phosphoric  acid  ;  the  number  given  in  the  table  for  this  acid 
is  taken  from  L.  Meyer  (Die  modernen  Theorien,  p.  489).     The  chapter  on  Che- 
mische  Massenwirkung  in  L.  Meyer's  book  should  be  studied  in  conjunction  with 
the  preceding  paragraphs  (203  —  235). 

2  Ostwald,  loc.  cit.  (*)  16.  425. 


442  CHEMICAL   KINETICS.  [§  237 

so  as  to  separate  the  factors  k  and  k'  (in  reactions  be- 
tween acids  and  bases)  into  two  parts,  one  depending  solely 
on  the  nature  of  the  acid  and  the  other  solely  on  the  nature 
of  the  base,  and  that  he  had  thence  deduced  the  conclusion 
that  the  affinity-constants  of  acids  are  proportional  to  the 
square  roots  of  the  velocities  of  the  reactions  brought  about  by 
them. 

Reviewing  the  whole  of  the  work  on  affinity  which  has 
passed  before  us,  we  are  I  think  justified  in  assenting  to 
Ostwald's  conclusion  that  the  specific  intensity  of  any  action 
brought  about  by  an  acid  is  conditioned  by  the  value  of  the 
affinity  of  that  acid  ;  or  as  it  is  put  by  Ostwald  in  another 
paper  (loc.  cit.  (2)  29.  57),  the  affinity-values  of  the  acids 
appear  as  constants  which  quantitatively  condition  the  chemi- 
cal actions  of  these  acids.  The  numbers  hitherto  obtained 
representing  the  relative  magnitudes  of  these  affinities  can  be 
regarded  only  as  approximate ;  no  reaction  has  yet  been 
found  entirely  free  from  secondary  changes,  nor  has  it  been 
possible  completely  to  eliminate  the  influence  of  these  se- 
condary changes  in  making  the  necessary  calculations.  Never- 
theless we  may  use  the  numbers  given  by  Ostwald,  more 
especially  those  derived  from  his  study  of  the  accelerating 
action  of  various  acids  on  the  decomposition  of  methylic 
acetate  by  water,  and  on  the  inversion  of  sugar  solutions,  in 
endeavouring  to  find  the  velocities,  and  final  states  of  equi- 
librium of  many  chemical  reactions. 

237.  Guldberg  and  Waage  did  not  attempt  to  do  more 
than  find  the  coefficients  of  affinity  of  various  reactions.  In 
their  use  of  the  expression,  a  coefficient  of  affinity  is  the 
resultant  of  the  actions  of  many  forces ;  Ostwald  has  analysed 
this  quantity,  and  has  endeavoured  to  assign  to  each  member 
of  the  changing  system  a  definite  number  which  represents 
the  share  of  the  total  result  belonging  to  that  constituent. 
As  each  element  has  a  definite  atomic  weight,  and  each  atom 
has  a  definite  valency,  and  as  these  numbers  sum  up  a  great 
deal  of  information  regarding  the  properties  of  the  element 
and  its  compounds  when  looked  at  from  a  statical  point  of 
view ;  so  each  chemical  substance  appears  to  have  a  definite 


§§238,239]  AFFINITY.  443 

affinity-constant,  and  this  number  conveys  much  information 
regarding  the  substance  when  regarded  from  a  kinetical 
stand-point.  These  affinity-constants  are  true  equivalents ; 
they  express  power  of  doing  definite  amounts  of  chemical 
work.  It  was  for  such  numbers  that  Bergmann  sought,  but 
sought  in  vain  ;  they  have  at  last  been  found,  or,  at  any  rate, 
we  have  been  shewn  how  they  are  to  be  found,  by  following 
in  the  steps  of  Bergmann's  great  opponent,  Claud  Louis 
Berthollet l. 


SECTION  2.     Thermal  and  other  methods  of  studying  affinity. 

238.  The   subject    of    affinity   has   thus   far   been   con- 
sidered, for  the  most  part,  apart  from  any  kinetic  theory  of 
chemical  action.     But  it  is  scarcely  possible  to  be  satisfied 
with  this  treatment.     We  cannot  but  attempt  to  form  some 
mental  image  of  the  molecular  and  atomic  mechanism  of  the 
changes  which   are  conditioned    by  the   affinities   of  bodies 
exerting  chemical  action  on  each  other.      Is  affinity,  in  the 
last  analysis,  to  be  ascribed  to  attractions  between  atoms  ;  or 
is  it  due  to  the  electrical  conditions  of  different  atoms  ?    How 
far  do   measurements   of  the  quantities   of  heat  evolved,  or 
absorbed,  during  chemical  operations,  afford  an  insight  into 
the  nature  of  these  processes  ?     Questions  of  this  kind  cannot 
be  overlooked,  however  difficult,  or  even  impossible,  it  may 
be  at  present  to  answer  them. 

239.  The  attempts  which  have  been  made  to  apply  the 
data  of  thermal  chemistry  to  the  problems  of  affinity  have  gene- 
rally been  based  on  the  hypothesis,  that  affinity  is  an  attraction 
between    atoms    which   is   dependent    on   variations   in   the 
potential   energies  of  these  atoms.     On  this  hypothesis,  the 
thermal    changes   which   accompany   definite   chemical    pro- 
cesses may  be  regarded  as  affording  measurements   of  the 
change  of  potential  into  kinetic  energy  which  proceeds  along 
with  the  rearrangement  of  the  atoms  of  the  elements  con- 
stituting the  chemical  systems. 

1  Compare  Mills,  Phil.  Mag.  (5)  1.    13.  with  Ostwald,  Journal  filr  prakt. 
Chemie  (2)  29.  57. 


444  CHEMICAL   KINETICS.  [§  239 

But  even  if  this  is  granted,  it  is  at  present  impossible  to 
make  much  use  of  this  means  of  measuring  the  energy-change 
in  question. 

Take  a  simple  case.  Given  the  heat  evolved  during  the 
change  of  2  parts  by  weight  of  gaseous  hydrogen  and  16  parts 
of  oxygen  into  18  parts  of  liquid  water,  we  have  the  difference 
between  the  energies  of  the  two  systems,  (i)  gaseous  H2  +  O, 
and  (2)  liquid  H2O,  as  measured  by  the  amount  of  heat  appear- 
ing in  the  calorimeter.  But  a  part  of  the  energy-difference,  as 
thus  determined,  is  due  to  the  change  of  gaseous  into  liquid 
water,  and  another  part  to  the  contraction  which  occurs  when 
two  volumes  of  hydrogen  and  one  of  oxygen  combine  to 
produce  two  volumes  of  water-gas1. 

In  the  majority  of  chemical  operations,  the  physical 
changes  are  more  complex  than  in  this  instance.  Different 
fractions  of  the  total  quantities  of  heat  measured  by  the 
calorimeter  are  connected  with  changes  in  the  densities,  the 
crystalline  forms,  the  thermal  capacities,  or  generally,  with 
changes  in  the  disgregation 2  of  the  substances  taking  part  in 
the  chemical  processes  for  which  thermal  values  are  required. 
But  we  are  not,  generally  speaking,  able  to  measure  the 
thermal  change  which  accompanies  a  disgregation-change. 
Indeed  we  cannot  always  decide  whether  the  value  of  this 
part  of  the  total  thermal  change  is  equal  to,  greater,  or  less 
than,  the  value  of  that  part  which  measures  the  affinities  of 
the  chemically  reacting  substances3. 

1  For  methods  of  calculating  these  two  parts  of  the  total  loss  of  energy  see 
Naumann,  Thermochemie  217 — 219  ;  and  also  Lothar  Meyer,  loc.  cit.  430 — 434. 

2  Clausius,  Pogg.  Ann.  116.  79,  &c.     Disgregation  is  a  quantity  depending  on 
the  arrangement  in  space  of  the  molecules  of  a  substance  ;   it  expresses  to  what 
extent  the  separation  of  the  molecules,  which  is  brought  about  by  the  action  of 
heat,  has  been  accomplished.    The  disgregation  of  a  body  is  greater  in  the  gaseous 
than  in  the  liquid,  and  greater  in  the  liquid  than  in  the  solid  state.     The  disgre- 
gation may  change  without  an  alteration  of  the  chemical  composition  or   the 
physical  state  of  the  body ;  thus,  when  a  gas  expands,  its  disgregation  increases. 
As  a  rule,  disgregation  increases  when  the  distance  between  the  molecules  of  a 
substance  is  increased.     Compare  Horstmann,  Annalen,  170.  195  ;  also  Naumann, 
loc.  cit.  209.      L.  Meyer  (loc.   cit.  429)  considers  Disgregation  as  equivalent  to 
degree  of  division  ( Vertheilungsgrad). 

3  Favre  and  Valson's  experiments  shew  that  the  thermal  changes  attending  the 
contraction  of  solutions  in  which  various  salts  are  formed  and  dissolve,  are  very 


§§240,24 1]  AFFINITY.  445 

240.  Even  in  cases  of  dissociation,  brought  about  by  the 
supply  of  energy  in  the  form  of  heat,  it  is  not  at  present 
possible  to  separate  the  energy  used  in  effecting  disgregation- 
changes  from  that  entirely  employed  in  separating  the  mole- 
cules into  less  complex  molecules,  or  into  atoms. 

But  even  if  this  could  be  done,  a  difficulty  would  still 
remain. 

Take  the  formation  of  gaseous  hydriodic  acid  from  gaseous 
hydrogen  and  iodine  ;  the  purely  chemical  reaction  is  not  fully 
represented  by  the  statement,  H  -f  I  =  HI,  but  rather  by  the 
equation,  H2-f- 12  =  2HI,  which  is  divisible  into  two  parts  ; 

(1)  H2  +  I2=H  +  H  +  I  +  I, 

(2)  H  +  H  +  I  +  I  =  2HI. 

The  problem  presented  is,  to  measure  the  energy-change 
which  accompanies  the  second  part  of  this  chemical  change. 
But  the  calorimetric  determinations  hitherto  made  furnish  no 
means  for  separating  the  total  thermal  value  into  its  con- 
stituent parts.  A  number  is  obtained  which  is  the  sum  of  two 
quantities  neither  of  which  is  known. 

241.  But  there  is  a  more  far-reaching  objection  to  many 
of  the  conclusions  regarding  affinity  which  have  been  drawn 
from   thermal   measurements.     It   is,   to   say   the   least,   im- 
probable, that  affinity  consists  of  an  attraction  between  atoms, 
depending  on  the  energy  of  position  of  these  atoms.     The 
atoms  of  which  a  molecule  is  composed  must  be  regarded  as 
in  motion  within  the  molecule ;    but  of  the  nature  of  this 

large.     See  Watts's  Diet.  2nd  Supplt.  -292  et  seq.;  and  3rd  Supplt.  983.     See  also 
for  more  details  Die  modernen  Theorien  der  Chemie,  (4th  ed. )  p.  436. 

Berthelot's  'law  of  maximum  work '  (see  book  I.  chap.  IV.  par.  133)  is  based 
on  the  assumption  that  affinity  is  a  form  of  potential  energy.  Meyer  shews  that 
there  are  cases  where  this  law  cannot  hold  good,  even  when  we  assume  that  all 
actions,  other  than  the  attractions  between  atoms,  are  eliminated.  For  a  fuller 
discussion  of  the  connections  between  this  law  and  affinity  see  L.  Meyer,  loc.  cit. 
pp.  440 — 460.  That  a  degradation  of  energy  is  an  invariable  accompaniment  of  a 
chemical  action,  occurring  by  itself,  is  certain,  but  it  is  not  the  case  that  an  opera- 
tion involving  degradation  of  energy  necessarily  occurs.  A  chemical  change 
between  gases,  involving  degradation  of  energy,  may  be  rendered  impossible  by 
causing  the  gases  to  expand,  and  this  although  the  total  heat  evolved  during  the 
operation  is  almost  the  same  whether  the  gases  are  expanded  or  condensed.  See 
Lord  Rayleigh,  Proc.  R.  I.  March  5,  1875. 


446  CHEMICAL   KINETICS.  [§§  242,  243 

motion  we  know  little  or  nothing.  A  feasible  hypothesis  is 
that  the  motion  is  such  as  produces  a  constant  change  of 
potential  into  kinetic  energy,  and  vice  versa.  But  if  this  view 
is  adopted,  the  same  compound  will  be  more  or  less  ready  to 
undergo  chemical  change,  according  to  the  phase  (see  ante, 
chap;  II.  par.  193,  p.  395)  in  which  it  is.  Let  AB,  a  diatomic 
molecule  of  a  gas,  collide  with  C,  a  monatomic  molecule  of  a 
gas;  more  than  one  change  may  occur;  AC  and  B  may  be 
produced  although  the  affinity  of  C  for  A  is  less  than  that  of 
C  for  B.  The  motions  of  the  atoms,  and  hence  the  relations 
between  their  potential  and  kinetic  energies  at  any  moment, 
will  be  conditioned  by  the  temperature,  among  other  causes. 
In  cases  more  complex  than  that  just  considered,  e.g,  in  the 
reactions  between  two  diatomic  gaseous  molecules,  AB  and 
CD,  it  is  not  at  present  possible  to  separate  the  action  of 
heat,  in  bringing  the  molecules  into  phases  whereat  chemical 
change  occurs,  from  the  action  of  affinity  pure  and  simple. 

242.  Thus,  we  come  back  to  the  statement,  already  in- 
sisted on  in  book  I.,  that  there  is  no  essential  difference  of 
kind  between  so-called  endothermic  and  exothermic  actions  *. 

Until  there  is  a  more  definite  kinetic  theory  of  affinity 
than  has  yet  been  proposed,  it  will  not  be  possible  to  apply 
thermal  methods,  except  in  a  general  and  broad  way,  to  the 
questions  suggested  by  the  term  affinity. 

243.  Every  chemical    change   involves  a  degradation  of 
energy,  but  chemical  energy,  of  whatever  form,  cannot  be 
entirely  run  down  into  heat. 

This  subject  has  been  considered  by  Helmholtz2. 
The  action  of  chemical  forces  gives  rise  not  only  to  heat, 
but  also  to  other  forms  of  energy,  and,  in  the  latter  cases, 

1  See  L.  Meyer,  he.  cit.  447 — 448.     Compare  also  book  i.  chap.  iv.  pars.  119, 
and    133;   also   book   n.  chap.    n.   section   2,   especially  par.    193.     Thomson's 
'  Theoretische  Betrachtungen  iiber  die  Dynamik  der   chemischen   Processe,'   in 
Thermae  he  misc  he  Untersuchungen  2.  468 — 474,  should  also  be  carefully  studied. 
See  also  in  connection  with  this,  Rathke,  Uber  die  Principien  der  Thermochemie, 
und  ihre  Anwendung  (Halle,  1881).     There  is  also  an  abstract  of  an  interesting 
paper  by  Potilitzin  in  Ber.  14.  2044. 

2  'Die  Thermodynamik  chemischer  Vorgange,'  Sitzber.  der  Wiss.  Akad.  zu 
Berlin^  1882;  see  Wissenschaftliche  Abhandlungen,  2,  958. 


§  243]  AFFINITY.  447 

sometimes  without  a  change  of  temperature  bearing  any 
kind  of  relation  to  the  magnitude  of  the  actions  between  the 
changing  substances ;  e.g.  in  the  performance  of  work  by 
the  battery.  Hence,  we  must  distinguish,  in  chemical  pro- 
cesses, between  those  parts  of  the  chemical  energy  which  are 
freely  changeable  into  other  forms,  and  those  which  can  only 
be  produced  in  the  form  of  heat.  The  former  is  called,  by 
Helmholtz,  the  free  energy,  the  latter  the  boiind  energy  (freie 
und gebuudene  Energie}.  The  bound  energy  is  the  difference 
between  the  total  internal  energy  and  the  free  energy. 
Changes  proceeding  of  themselves  from  a  state  of  rest,  and 
at  a  uniform  temperature,  without  the  help  of  energy  from 
without  the  system,  can  only  proceed  in  directions  such  that 
the  free  energy  decreases.  Assuming  the  universality  of  the 
second  law  of  thermodynamics,  it  follows  that  the  direction  in 
which  the  chemical  affinity  of  a  substance  can  act  depends 
on  the  value  of  the  free  energy,  and  not  on  that  of  the  total 
energies  which  make  themselves  known  by  the  production  of 
heat.  The  free  energy  can  only  be  calculated  in  completely 
reversible  changes.  Electrolytic  decompositions  with  un- 
polarised  electrodes  serve  well  for  this  purpose ;  indeed  it  was 
when  examining  the  relations  between  the  electromotive  force 
of  such  cells  and  the  chemical  changes  which  proceed  within 
them  that  Helmholtz  was  led  to  the  conception  of  free  chemi- 
cal energy. 

In  all  isothermal  changes  work  is  done  only  at  the  cost  of 
the  free  energy;  in  all  adiabatic  changes  work  is  produced  at 
the  cost  both  of  the  free  and  the  bound  energy  of  the  system. 
In  all  other  cases,  external  work  is  carried  on  at  the  cost  of 
the  free  energy,  and  loss  of  heat  at  the  cost  of  the  bound 
energy ;  and  for  every  rise  of  temperature  of  the  system,  free 
is  changed  into  bound  energy.  This  last  case  may  occur  in 
irreversible  processes,  so  that  free  energy  is  changed  into 
kinetic  energy  which  again  may  be  converted,  by  friction,  &c., 
either  wholly  or  in  part  into  heat.  In  such  a  case  the  heat 
evolved  in  the  change  from  the  initial  to  the  final  state  of  the 
system  represents  the  difference  between  the  tptal  internal 
energies  of  the  system.  Now  this  difference  is  the  quantity 


448  CHEMICAL   KINETICS.  [§  244 

measured  in  investigations  of  thermal  changes  accompanying 
chemical  processes ;  but  the  work  done  by  the  free  energies 
of  the  system,  the  free  work  (freie  Arbeit),  which  determines 
the  direction  of  the  chemical  change,  is  different  from  this, 
and  cannot  be  measured  by  merely  finding  the  total  quantity 
of  heat  evolved. 

244.  But  it  may  be  admitted  that  chemical  affinity,  con- 
sidered as  some  form  of  atomic  energy,  cannot  as  yet  be 
satisfactorily  measured  by  thermal  methods,  and  at  the  same 
time  it  may  be  held  that  thermal  measurements  do  throw 
light  on  the  differences  between  the  affinities  of  substances  in 
various  analogous  reactions,  using  the  term  affinity  in  a  sense 
similar  to  that  wherein  it  is  employed  by  Guldberg  and 
Waage. 

Thus,  let  us  compare  the  thermal  values  of  the  reactions 
which  occur  in  the  formation  of  gaseous  hydrochloric,  hydro- 
bromic,  and  hydriodic  acids  from  gaseous  hydrogen,  and 
gaseous  chlorine,  gaseous  bromine,  and  gaseous  iodine  respec- 
tively1. The  change  is  expressed  in  thermal  notation  as 
[H,  X] ;  the  following  are  the  numbers  to  be  compared, 

[H,  X]  gaseous. 
X=  Cl  =  22,000  gram-units  -f  • 
^T=Br=  12,000          „          +. 
X=l    =   1,530          „ 

Are  the  affinities  of  Cl,  Br,  and  I  for  H  in  the  proportion  of 
the  numbers  22  :  12  :  —  1-5  ? 

When  the  reaction  is  written,  as  our  former  study  of 
chemical  changes  has  taught  it  ought  to  be  written,  in  the 
form  [H2,  X*]  =  2[H,  X]  -  [H,  H]  -  [X,  X],  we  see  that  the 
numbers  given  do  not  measure  the  affinities  of  the  atoms  of 
chlorine,  bromine,  and  iodine  for  that  of  hydrogen.  We  have 
at  present  no  means  for  measuring  the  absorptions  and  evolu- 
tions of  heat  the  sums  of  which  are  represented  by  the 
numbers  22,000,  12,000,  and  —1530.  We  are  not  even  jus- 
tified in  concluding  that  the  value  —  [X,  X]  is  the  same 
whether  X  =  Cl,  Br,  or  I ;  indeed  experiments  on  the  densities 

1  Compare  Jahn,  Die  Gnmdsatze  der  Thermochemie^  35 — 43. 


§  245]  AFFINITY.  449 

of  these  gases  at  high  temperatures  rather  tend  to  shew  that 
this  assumption  is  untenable.  But  if  the  term  affinity  is  used 
as  meaning  the  resultant  of  the  actions  of  the  various  forces 
which  come  into  play  in  any  chemical  change,  eliminating  as 
far  as  possible  actions  which  are  manifestly  physical,  then 
I  think  we  may  say  that  the  differences  between  the  affinities 
concerned  in  the  three  strictly  comparable  reactions,  viz.  for- 
mation of  gaseous  hydrochloric,  hydrobromic,  and  hydriodic 
acids,  from  their  gaseous  elements,  are  expressed  by  the 
differences  between  the  numbers  22,  12,  and  —  1*5. 

245.  If  this  conclusion  is  sound,  then  the  differences 
between  the  thermal  values  of  analogous  chemical  changes 
in  which  the  same  elements  take  part  should  be  capable 
of  being  represented  as  multiples  of  a  common  number. 

Here  are  some  data  suited  for  our  purpose. 

(i)[H,^f,Aq];^'=Cl  =  39,3i5:^r=Br=28,37o:A'=I  =  i3,i7ogrm.-units  +  . 

.'.  [H,  Cl,  Aq]-[H,  Br,  Aq]  =  10,945, 
and  [H,  Cl,  Aq]-[H,  I,  Aq]    =26,145. 

(2)[K,^r,Aq];^T=Cl=ioi,i7o:^r=Br=9o,23o:^Y=I  =  75,o2ogrm.-units  +  . 

.-.  [K,  Cl,  Aq]-[K,  Br,  Aq]=  10,940, 
and  [K,  Cl,  Aq]-[K,  I,  Aq]    =26,150. 

Also  [Na,  Cl,  Aq]-[Na,  Br,  Aq]=  10,930, 
and  [Na,  Cl,  Aq]-[Na,  I,  Aq]    =26,150. 

The  difference  between  the  heat  of  formation,  in  solution, 
of  a  chloride  and  an  analogous  bromide,  is  10,940  units ;  and 
that  between  a  chloride  and  an  analogous  iodide  is  26,150 
units. 

Now  these  differences  reappear  in  the  following  data. 

FM,  CL ,  Aq]  -  FM.  Br» ,  Aq]  =  2  x  10,940  1     . 

1  rn/  ^.i     AT    TUT   T      A   -i  *         \  when  M  =  Ca,  Sr.  or  Cu. 

and  [M,  C12,  Aq]-[M,  I2,  Aq]    =2x26,150] 

Here  we  notice  a  constant  thermal  value  attending  the 
substitution  of  one  halogen  by  another,  the  metallic  radicle 
being  unchanged ;  now,  if  the  halogen  remain  the  same,  is 
there  a  constant  thermal  value  for  the  substitution  of  one 
metal  by  another,  chemically  analogous,  metal  ? 

M.  C.  29 


450  CHEMICAL  KINETICS.  [§  246 

The  following  data  shew  that  there  is  such  a  constant 
thermal  value. 

(  4,660  when  X=  Cl, 

[K,  X,  Aq]   -[Na,  X,  Aq]  =1  4,650  when  X=Er, 

[  4,620  when  X=l ; 

and  [Sr,  X2,  Aq]  -  [Ca,  X2,  Aq]  =  2  x  4,020  when  X=  Cl,  Br,  or  I. 

The  thermal  values  of  another  series  of  analogous  reactions 
are  given  in  the  following  table. 

Heats  of  oxidation  of  N2O2,  N2O3,  and  N2O4. 

[N2O4,  Aq,  O]  =       18,320  gram-units  +  . 
[N203,Aq,  02]  =  2x  18,320 


[N202,Aq,0]  =2x18,1 65 
[N*0*,Aq,  0*]  =  3  x  18,215 
[NW,Aq,03]  =  4x  18,243 

The  data  presented  in  this  paragraph  justify  the  conclu- 
sion that  a  study  of  the  thermal  values  of  analogous  chemical 
changes  occurring  between  similar  elements  is  fitted  to  throw 
light  on  the  differences  between  the  affinities  of  the  substances 
taking  part  in  these  reactions. 

246.  The  theory  of  vortex  atoms  promises  to  help  to- 
wards a  solution  of  the  problem  of  affinity. 

The  theory  has  been  applied  to  chemical  combinations  by 
J.  J.  Thomson  \ 

A  compound  molecule  of  a  gas  is  regarded  by  this  theory 
as  consisting  of  two,  or  more,  vortex  rings.  This  united  vortex 
ring  will  separate  into  its  parts  when  subjected  to  a  disturbing 
influence,  such  as  the  action  due  to  other  vortex  rings  in  the 
neighbourhood.  The  theory  thus  leads  to  a  conception  of 
chemical  combination  closely  resembling  that  enunciated  by 
Williamson,  and  afterwards  altered  and  developed  by  Pfaundler 
(chap.  II.  pars.  1 86,  187).  But  for  a  compound  gas  to  be  more 
than  a  mere  mixture  of  elementary  gases  it  is  necessary  that 
'  the  mean  time  during  which  an  atom  is  paired  with  another 
*  of  a  different  kind,  which  we  shall  call  the  paired  time, 

1  On  the  motion  of  vortex  rings.     The  Adams  Prize  Essay  for   1882.     See 
especially  p.  114  et  seq. 


§247]  AFFINITY.  45 1 

'  should  be  large,  compared  with  the  time  during  which  it  is 
'  alone  and  free  from  other  atoms,  which  we  shall  call  the 
'free  time'  (loc.  cit.  p.  115). 

The  ratio  of  paired  to  free  time  will  be  diminished  by  any 
disturbance  to  which  the  gas  is  subjected;  when  the  diminu- 
tion is  carried  past  a  certain  amount,  the  gas  is  decomposed. 

Now  'the  pairing  of  two  atoms is  attended  by  a  large 

'increase  in  the  translatory  energy;'  but  as  these  atoms  are 
only  paired  for  a  time,  '  the  whole  increase  in  the  translatory 

'energy  of  a  large  number  of  molecules  will  depend on 

'  the  ratio  of  the  paired  to  the  free  times '  of  the  vortex 
atoms  which  form  the  molecules  of  the  substance  (loc.  cit. 
p.  1 1 6).  The  value  of  this  ratio  in  the  case  of  an  elementary 
gas  will  to  a  great  extent  condition  the  chemical  properties  of 
that  gas ;  it  will  also  determine  whether  chemical  combination 
shall  or  shall  not  occur  between  two  gases,  and  if  it  occurs,  it 
will  fix  the  proportions  between  the  amounts  of  the  various 
compounds  produced.  An  elementary  gas  will  readily  enter 
into  chemical  combination,  only  when  the  ratio  of  free  to 
paired  time  is  larger  for  the  molecule  of  the  element,  than  for 
that  of  the  compound  produced.  The  value  of  the  ratio  in 
question  may  therefore  afford  a  measure  of  the  relative 
affinities  for  each  other  of  the  atoms  of  various  compound 
molecules  \ 

247.  In  the  general  remarks  made  on  the  subject  of 
affinity  in  par.  202  it  was  said  that  attempts  might  be  made 
to  obtain  measurements  of  affinities  by  electrical  methods. 
I  wish  now  to  draw  the  student's  attention  to  some  of  the 
more  important  of  these  attempts. 

The  views  of  Davy  and  of  Berzelius  regarding  the  con- 
nections between  electrical  and  chemical  actions  have  already 
been  referred  to  (book  I.  chap.  II.  pars.  46  to  48). 

Faraday  discovered  that  when  an  electric  current  passes 
through  an  electrolytic  cell,  the  amount  of  decomposition  is 
definite  for  each  element  of  the  electrolyte,  and  is  dependent 
on  the  quantity  of  electricity  which  is  transmitted.  Let  e  be 
the  mass  of  an  element  separated  from  any  of  its  salts  by  the 

1  For  more  details  see  J.  J.  Thomson,  loc.  cit. 

29 — 2 


45  2  CHEMICAL  KINETICS.  [§  247 

passage  of  one  unit  of  electricity.  Then  e  is  called  the  electro- 
chemical equivalent  of  that  element.  Since  unit  quantity  of 
electricity  is  transmitted  by  unit  current  in  unit  time,  we  may 
say  that  one  electrochemical  equivalent  of  an  element  is 
separated  from  any  of  its  combinations  by  unit  current  in 
unit  time. 

The  minute  verification  of  this  law  is  still  being  worked 
out  experimentally. 

In  the  course  of  his  applications  of  the  conception  of  the 
conservation  of  energy,  Joule  undertook  a  series  of  researches 
on  the  *  energetics'  of  the  electric  current1.  The  case  of  the 
passage  of  a  current  through  a  wire  was  considered,  and  the 
quantity  of  heat  evolved  was  found  to  be  expressed  by  the 

equation 

H=CE, 

where  H  is  the  quantity  of  heat  developed  per  second,  and 
C  and  E  are  the  current  and  the  electromotive  force  re- 
spectively. 

Since  Joule  had  himself  shewn  that  heat  is  changeable 
into  work,  the  equation  took  the  form 


where  /  =  the  mechanical  equivalent  of  heat. 

The  phenomena  attending  the  evolution  of  heat  during 
the  passage  of  a  current  through  an  electrolyte  were  then 
examined  by  Joule,  and  it  was  shewn  that  the  total  quantity 
of  heat  could  be  separated  into  two  parts.  One  part  was 
expressible  as  the  result  of  overcoming  ordinary  resistance  in 
accordance  with  his  previous  law,  and  the  other  part  was  due 
to  chemical  changes  in  the  cell.  He  then  determined  the 
quantity  of  heat  evolved,  during  a  given  time,  in  a  process 
of  electrolysis  by  a  current  of  given  strength  ;  then,  by  ap- 
plying Ohm's  law,  and  the  law  stated  connecting  heat  with 
resistance  and  current,  he  found  the  heat  which  would  have 
been  evolved,  had  a  wire  with  resistance  equal  to  that  of 
the  electrolyte  been  substituted  for  the  electrolyte.  The 
difference  between  these  two  quantities  of  heat  is,  Joule  said, 

1    Phil.  Mag.  20.  98;   22.  204;    and  do.  (2)  3.  481.     See  also  the  article 
'Electricity'  in  Encycl.  Brit.  Vol.  8.  (Qth  Ed.)  pp.  88-92. 


§§  248,  249]  AFFINITY.  453 

'  equivalent  to  the  heat  which  is  due  to  the  reverse  chemical 
'  combination  by  combustion  or  other  means '  (loc.  cit.  (2)  3. 
494). 

248.  The    problem  was  further  considered   by  Sir   W. 
Thomson1.     His  reasoning  was  somewhat  as  follows. 

Let  unit  quantity  of  electricity  pass  through  a  cell  of 
infinitely  small  resistance ;  then,  by  Joule's  law,  the  work 
done  by  the  current  is  equal  to  E,  the  electromotive  force. 
But  '  e  gram  of  one  of  the  elements  of  the  electrolyte  has 
been  electrolysed,  in  accordance  with  Faraday's  law.  Let  6 
be  the  quantity  of  heat  developed  by  the  combination  of  one 
gram  of  this  element  to  reproduce  the  electrolyte,  then,  ac- 
cording to  Thomson,  since  no  work  is  expended  in  any  other 

part  of  the  circuit, 

E 
E=Je6,  and  therefore  0=-=-. 

To  realise  this  equation  in  practice  a  great  many  corrections 
have  to  be  applied. 

This  formula  presents  us  with  an  electrical  method  for 
determining  the  heats  of  combination  of  various  elements,  or, 
we  may  say,  the  energy-changes  attending  the  formation  of 
various  compounds.  In  Joule's  papers,  the  values  of  the 
quantity  represented  by  6  were  regarded  as  affording  measures 
of  '  the  intensities  of  affinity '  of  different  substances  (loc.  cit. 
20.  99) ;  but  we  have  seen  that  this  cannot  now  be  held, 
except  the  term  '  affinity '  is  used  in  a  very  wide  sense. 

249.  Wright  has  applied  Joule  and  Thomson's  method  of 
research,  and  has  endeavoured  to  determine  '  chemical  affinity 
'  in  terms  of  electromotive  force  V 

In  Wright's  use  of  the  term,  the  'affinity'  between  the 
constituents  of  a  compound  is  measured  by  the  work  done  in 
separating  the  compound  into  these  constituents.  This  work 
can  be  measured  by  electrical  methods ;  thus,  Wright  says, 
'  the  affinity  between  the  final  products  of  an  electrolyte,  i.e. 
*  the  work  done  in  resolving  it  into  these  final  products 

1  Phil.  Mag.  for  December,  1851  :   see  Mathematical  and  Physical  Papers  I. 
472. 

2  Phil.  Mag.  (5)  9.  237,  331:   11.  169,  261,  348:  13.  265:  14.  188:  16.  25. 
See  also  a  general  account  of  his  work  to  the  end  of  1880  in  Chem.  News,  42.  249. 


454  CHEMICAL  KINETICS.  [§  249 

'  is  readily  determinable,  by  determining  the  difference  of 
'  potential  subsisting  between  the  electrodes,  and  the  heat 
'  evolved  as  such,  during  the  electrolysis  of  a  gram-equivalent ' 
(Chem.  News,  loc.  cit.}. 

But  in  a  process  of  electrolysis,  the  electrolyte  is  first 
separated  into  primary,  or  nascent  products,  which  are  such 
that  their  change  into  the  secondary,  or  final  products  is 
attended  with  evolution  of  heat.  The  E.M.F.  required  to 
separate  the  electrolyte  into  the  nascent  products  would  there- 
fore be  numerically  greater  than  the  E.M.F.  required  to 
separate  it  into  the  final  products.  Moreover,  the  E.M.F. 
required  to  break  up  a  given  electrolyte,  under  given  con- 
ditions, into  the  nascent  products  of  electrolysis,  varies,  because 
of  the  occurrence  of  secondary  physical  and  chemical  actions 
between  the  electrodes  and  the  dissolved  gases,  &c.  Heat 
is  generated  in  these  secondary  changes,  and  the  energy  thus 
produced  diminishes  the  work  that  would  otherwise  be  done 
by  the  current  in  effecting  electrolysis.  Hence  the  E.M.F. 
which  corresponds  to  the  total  electrolytic  work  actually 
done  by  the  current,  is  less  than  the  constant  amount  which 
would  be  required  were  the  process  not  complicated  by 
secondary  reactions1.  Wright  attempts  to  find  the  value  of 
that  part  of  the  E.M.F.  which  corresponds  to  the  secondary 
changes,  (i)  when  none  of  the  products  of  electrolysis  are 
developed  in  the  nascent  state,  and  (2)  when  the  products 
are  entirely  developed  in  this  state2.  The  determination 
becomes  very  difficult  in  the  latter  case :  if  it  can  be  suc- 
cessfully made,  we  shall  have  data  for  finding  the  E.M.F. 
produced  by  the  combination  of  the  constituents  of  certain 
compounds,  starting  with  these  constituents  in  the  nascent 
state.  But  as  the  nascent  state  of  a  substance  most  proba- 
bly represents  its  condition  when  the  great  majority  of  the 
molecules  are  separated  into  atoms,  it  follows  that  Wright's 
determinations  of  the  two  parts  of  the  E.M.F.  concerned  in 

1  Wright,  Phil.  Mag.  (5)  13.  265.  For  a  short  and  clear  statement  of  the 
whole  of  this  subject,  see  Clerk  Maxwell's  Elementary  Treatise  on  Electricity, 
pars.  182 — 192. 

3  See  Chem.  News,  loc.  cit.  p.  253. 


§  250]  AFFINITY.  455 

electrolytic  decompositions,  if  successfully  conducted,  must 
throw  considerable  light  on  the  actions  of  the  forces  which 
condition  the  combinations  of  atoms,  and  therefore,  on  the 
most  profound  parts  of  the  problem  of  chemical  affinity. 

250.  The  subject  of  the  connection  between  the  forces 
which  come  into  play  in  chemical  and  electrical  phenomena, 
has  been  considered  by  Helmholtz  in  the  Faraday  Lecture  for 
iSSi1. 

Faraday's  statement  that  'the  equivalent  weights  of 
'bodies  are  simply  those  quantities  of  them  which  contain 

'equal  quantities  of  electricity, or,  if  we  adopt  the  atomic 

'  theory  or  phraseology,  then  the  atoms  of  bodies  which  are 
'  equivalent  to  each  other  in  their  ordinary  chemical  action, 
'  have  equal  quantities  of  electricity  naturally  associated  with 
'  them 2,'  is  developed  by  Helmholtz  in  the  light  of  modern 
conceptions  of  molecular  structure. 

Helmholtz  regards  each  monovalent  atom,  or  group  of 
atoms,  forming  an  ion,  as  moving  about  with  an  equivalent 
of  electricity,  each  divalent  atom  (or  ion)  with  two  equi- 
valents of  electricity,  and  so  on.  An  ion  may  be  attracted 
to  the  surface  of  an  electrode,  and  if  the  electromotive 
force  is  sufficient,  the  electric  charge  of  the  ion  may  be 
attracted,  and  so  the  ion  may  itself  become  electrically 
neutral.  A  gas,  e.g.  hydrogen,  evolved  during  electrolysis 
is  electrically  neutral ;  this  may  be  because  each  atom  is 
electrically  neutralised,  or  more  probably,  because  neutrality 
is  obtained  by  the  union  of  one  atom,  with  its  positive 
charge,  with  another  atom,  carrying  a  negative  charge 
of  electricity.  Helmholtz  then  shews  by  experiment  that 

'electrolytic  conduction  is  not necessarily  connected  with 

'a  small  resistance  to  the  current;'  and  that  'the  connection 
'  of  electric  and  chemical  force  is  not  at  all  limited  to  the 
'  acid  and  saline  solutions  usually  employed '  (loc.  cit.  p.  293). 
But  why  is  the  electric  attraction  at  the  poles  of  a  battery  of, 
say,  two  Daniell's  cells,  so  small,  when  this  combination  is 
nevertheless  able  to  decompose  water,  a  liquid  in  the  forma- 

1  C.  S.  Journal,  Trans,  for  1881.  277. 

3  Experimental  Researches  in  Electricity,  Series  vil.  par.  869. 


456  CHEMICAL  KINETICS.  [§  250 

tion  of  I  gram  of  which  from  its  elements  an  amount  of  heat 
equal  to  1,600,000  gram-metres  of  work  is  developed  ? 
Helmholtz  finds  the  answer  to  this  question  in  the  enormous 
electrical  charges  of  the  elementary  atoms.  He  calculates 
that  'the  electricity  of  I  milligram  of  water,  separated  and 
1  communicated  to  two  balls,  I  kilometre  distant,  would  pro- 
'duce  an  attraction  between  them  equal  to  the  weight  of 
'26,800  kilograms;'  or  comparing  'the  gravitation  acting 
'between  two  quantities  of  hydrogen  and  oxygen  with  the 
'attraction  of  their  electric  charges/  the  electrical  force  is 
71,000  billion  times  greater  than  the  gravitation  force  (loc.  cit. 
pp.  293 — 294).  A  very  small  battery  can  decompose  water, 
because  the  attracting  force  exerted  by  the  poles  on  the 
enormous  charges  of  the  atoms  of  hydrogen  and  oxygen  is 
very  great. 

Helmholtz  shews  by  various  experiments  that  an  electro- 
motive force  as  small  as  j^1^  Daniell  is  able  to  attract  the 
ions  to  the  electrodes  of  a  small  cell,  and  to  charge  these 
electrodes  as  condensers.  Indeed  no  phenomenon  has  been 
discovered  which  indicates  any  limit  to  the  smallness  of  the 
electromotive  force  which  is  able  to  do  this,  and  '  we  must, 
'therefore,  conclude  that  no  other  force  resists  the  motions  of 
'  the  ions  through  the  interior  of  the  liquid  than  the  mutual 
'attractions  of  their  electric  charges'  (loc.  cit.  p.  297).  The 
electric  attraction  produces  an  equal  distribution  of  the  oppo- 
site constituent  atoms  throughout  the  liquid,  which  is  thus 
electrically  as  well  as  chemically  neutralised. 

But  let  the  liquid  be  decomposed,  there  must  be  electrical 
attraction  between  the  ions  with  their  charges  of  electricity 
and  the  electrodes  of  the  battery.  If  this  attraction  is  not 
sufficient  to  deprive  the  ions  of  their  charges,  the  cation  is 
attracted  to,  and  retained  by  the  cathode,  and  the  anion  by 
the  anode,  with  a  force  so  great  that  no  diminution  of  pressure 
over  either  electrode  suffices  to  remove  the  ion.  But '  increase 
'  the  electric  potential  of  the  electrodes  so  that  the  electric 
'  force  becomes  powerful  enough  to  draw  the  electric  charge 
'  of  the  ions  over  to  the  electrode,'  and  the  ions  are  liberated 
as  gases,  or  diffuse  into  the  liquid.  If  the  ponderable  matter 


§  250]  AFFINITY.  457 

of  the  ions  were  attracted  by  the  electrodes,  this  attraction 
would  remain  after  discharge,  but  it  does  not,  therefore  '  we 
'  must  conclude  that  the  ions  are  drawn  to  the  electrodes  only 
'  because  they  are  charged  electrically '  (loc.  cit.  p.  299). 

The  mechanism  is  then  described  whereby  the  electrical 
force  is  concentrated  at  the  surface  of  electrodes,  until,  acting 
at  molecular  distances,  it  becomes  able  '  to  compete  with  the 
'  powerful  chemical  forces  which  combine  every  atom  with  its 
'  electric  charge,  and  hold  the  atoms  bound  to  the  liquid ' 
(p.  300). 

Helmholtz  then  develops  the  view  that  equivalents  of 
positive  and  negative  electricity  (using  the  language  of  the 
dualistic  hypothesis)  are  attracted  by  different  atoms  with 
different  forces ;  e.g.  the  atom  of  zinc  has  probably  a  greater 
attraction  for  positive  electricity  than  the  atom  of  copper  has 
for  negative  electricity.  These  attractive  forces  act  only 
through  molecular  distances.  This  hypothesis  of  'different 

*  degrees  of  affinity  between  the  metals  and  the  two  elec- 

*  tricities '  explains  the  facts  of  contact  electricity ;    e.g.  the 
greater  attraction  of  zinc  for  positive  electricity  than  of  copper 
for  negative  produces  chemical  decomposition  of  the  electro- 
lyte present,  and  electrical  equilibrium  is  not  possible  until 
this  decomposition  is  completed  (loc.  cit.  pp.  300 — 302)'. 

Each  atom  is  thus  regarded  as  charged  with  a  definite 
'equivalent  of  electricity/  A  divalent  atom  has  two  equi- 
valents, a  trivalent  atom  three  equivalents,  and  so  on,  but 
these  equivalents  are  held  to  the  atoms  by  varying  attractive 
forces.  A  compound  which  is  electrically  neutral  will  have 
each  equivalent  of  positive  electricity  neutralised  by  an  equi- 
valent of  negative  electricity  on  another  atom. 

'  I  think'  says  Helmholtz  'the  facts  leave  no  doubt  that  the 
'  very  mightiest  among  the  chemical  forces  are  of  electric 
'  origin.  The  atoms  cling  to  their  electric  charges,  and  op- 

*  posite  electric   charges  cling  to   each   other,  but  I   do  not 
4  suppose  that  other  molecular  forces  are  excluded,  working 
'  directly  from  atom  to  atom '  (loc.  cit.  pp.  302 — 303). 

1  Compare  also  Davy's  view,  as  quoted  in  book  I.  chap.  n.  par.  46. 


45 8  CHEMICAL   KINETICS.  [§§25I~ 3 

25 1.  Helmholtz  thus  presents  us  with  a  theory  of  chemical 
affinity  in  many  respects  resembling  that  held  by  Berzelius. 
We  are  taught  to  look  on  each  atom  as  carrying  with  it  a 
definite  quantity  of  positive  or  negative  electricity ;    but  in 
place  of  the  varying  '  intensity  of  polarity/  which  Berzelius 
regarded  as  closely  associated,  if  not  identical,  with  chemical 
affinity,  we  have  the  varying  attractive  force  with  which  the 
equivalents  of  electricity  are  held  by  different  atoms  \ 

252.  The  theory  of  chemical  equilibrium  propounded  by 
Pfaundler,  on  the   lines  of  that  of  Williamson,  is    quite  in 
keeping  with  the  electrical  theory  developed  by  Helmholtz, 
inasmuch  as  no  work  need  be  done  in  a  chemically  homo- 
geneous system  in  which  mutual  exchange  of  similar  atoms 
with  similar  electrical  charges  is  occurring  between  the  mole- 
cules which  constitute  the  system 2. 

253.  I  have  attempted,  in  the  preceding  paragraphs  of 
this  section  to  sketch  the  present  state  of  knowledge  regarding 
affinity,  and  at  the  same  time  to  indicate  the  methods,  and 
the  steps,  by  which  this  knowledge  has  been  gained. 

In  the  theory  of  Guldberg  and  Waage,  we  are  presented 
with  a  general  statement  of  the  influence  exerted  by  the 
relative  masses  of  the  substances  forming  a  chemically  active 
system  on  the  equilibrium  attained  by  the  system,  when  all  the 
constituents  are  free  mutually  to  act  and  react.  The  total 
chemical  change,  in  such  a  case,  is  the  sum  of  many  changes, 
each  of  which  may  be  regarded  as  determined  by  the  resultant 
of  the  actions  of  various  forces,  both  chemical  and  physical. 
Eliminating,  as  far  as  possible,  the  physical  actions,  Guldberg 
and  Waage  call  the  resultant  of  the  actions  of  the  chemical 
forces,  concerned  in  each  part  of  the  total  change,  the  coeffi- 
cient of  affinity  for  that  reaction.  The  equilibrium  of  the 
entire  system  is  determined  by  the  various  coefficients  of 
affinity,  and  by  the  active  masses  of  all  the  constituents.  If 
chemical  operations  are  chosen  for  study  which  consist,  as  far 
as  possible,  of  one  primary  and  one  reverse  change,  values 
may  be  found  for  various  coefficients  of  affinity  in  terms  of 
some  one  chosen  as  unity. 

1  Compare  book  I.  chap.  n.  par.  47.  *  See  Arrhenius,  Ber.  17.  49. 


§  253]  AFFINITY.  459 

But  these  coefficients  of  affinity  may  be  further  analysed. 
Ostwald  has  shewn  us  how  to  set  about  this,  in  the  case  of 
the  reactions  between  acids  and  bases.  When  two  acids  and 
a  single  base  react,  the  coefficient  of  affinity  for  the  reaction 
may,  according  to  Ostwald,  be  divided  into  two  parts,  one 
depending  only  on  the  nature  of  the  base  and  the  other  only 
on  the  nature  of  each  acid.  In  other  words,  each  acid,  and 
each  base,  exerts  a  specific  influence  on  the  course  of  the 
reaction  and  on  the  final  equilibrium  attained  by  the  system. 
By  pursuing  this  method  of  enquiry,  Ostwald  arrives  at 
certain  numbers  which  represent  the  relative  affinities  of  the 
acids  in  terms  of  that  of  hydrocloric  acid  taken  as  100.  The 
subsequent  researches  of  this  naturalist,  we  found,  on  the 
whole  confirmed  the  values  he  had  assigned  to  the  relative 
affinities  of  the  acids. 

But,  as  we  saw  in  par.  202,  measurements  of  the  changes 
of  energy  which  accompany  changes  in  the  distribution  of  the 
chemically  different  kinds  of  matter  of  a  system,  must  throw 
light  on  the  actions  of  the  forces  which  come  into  play  in 
these  changes.  Such  measurements  of  changes  of  energy  are 
best  accomplished  by  means  of  the  calorimeter.  We  found 
that  the  thermochemical  researches  of  Thomsen  on  the  phe- 
nomena which  occur  when  two  acids  and  one  base  mutually 
react,  lead,  practically,  to  the  same  conclusions  regarding  the 
relative  affinities  of  acids,  as  those  gained  by  Ostwald  by 
different  methods  of  investigation. 

But  the  energy-changes  which  accompany  chemical  re- 
actions are  regarded  by  the  molecular  theory  as  essentially 
connected  with  changes  in  the  arrangements  of  the  atoms  of 
the  elements  which  form  the  reacting  systems.  Hence,  what 
is  desired,  is,  if  possible,  to  measure  the  energy-changes  which 
occur  along  with  definite  actions  and  reactions  between  atoms. 
Now,  we  found  that  thermochemical  measurements  really  re- 
present the  sums  of  many  operations,  some  of  which  involve 
evolution  of  heat, and  some,  absorption  of  heat;  some  of  which 
again  are  physical  and  some  chemical. 

If  the  term  affinity  is  to  be  applied  only  to  the  transac- 
tions between  atoms,  when  viewed  from  the  side  of  one  kind 


460  CHEMICAL  KINETICS.  [§  253 

of  the  reacting  atoms,  then  thermal  methods  of  investigation 
cannot  at  present  help  us  much  to  a  knowledge  of  affinity. 
I  think  it  must  have  been  noticed  that  the  term  affinity 
appeared  to  be  continually  changing  its  meaning  in  the 
paragraphs  wherein  the  bearings  of  thermochemical  data  on 
this  subject  were  considered.  Sometimes  affinity  appeared  to 
be  only  another  term  for  chemical  change,  sometimes  it  was 
the  force  exerted  by  one  atom  on  another,  sometimes  it  was 
the  energy-change  accompanying  a  change  in  the  arrange- 
ment of  various  chemical  substances.  When  we  came  to 
glance  at  the  electrical  aspects  of  the  subject,  then  affinity 
appeared  as  nearly  if  not  quite  identical  with  electrical  forces. 
The  investigations  of  Helmholtz  seemed  to  shew  us  the  atoms 
of  every  element  carrying  with  them,  in  their  movements, 
definite  charges  of  electricity,  but  holding  these  charges  with 
a  force  which  varies  for  the  atom  of  each  element.  Chemical 
changes  appeared  to  be  very  largely  conditioned  by  the 
magnitudes  of  these  electrical  charges,  and  by  the  forces 
wherewith  the  charges  are  held  to  the  different  atoms. 

If,  in  the  light  of  these  investigations,  the  term  affinity  is 
still  to  be  employed,  it  must,  at  present,  have  a  meaning  some- 
what vague,  or  at  least  wide.  When  we  say  that,  under  given 
conditions,  this  compound  is  produced  rather  than  that,  or  more 
of  this  is  produced  than  of  that,  because  of  the  differences 
between  the  affinities  of  the  reacting  elements,  we  mean,  that 
the  final  arrangement  of  the  reacting  elements  is  conditioned 
by  the  mutual  actions  of  their  atoms,  and  that  these  actions 
are  largely  determined  by  the  electrical  charges,  and  electrical 
conditions,  of  those  atoms. 

Whether  the  term  affinity  should  be  employed  at  all,  with 
such  a  meaning  as  this,  is  open  to  doubt. 

As  long  as  we  deal  with  certain  numbers  representing 
the  relative  affinities  of  definite  substances,  we  are  on  firm 
ground ;  these  numbers  summarise  a  great  deal  of  informa- 
tion about  the  substances  themselves.  But  when  we  attempt 
to  frame  a  general  theory  of  affinity,  we  are  practically 
endeavouring  to  construct  a  general  theory  of  chemical  action, 
and  it  is  very  questionable  whether  the  former,  apparently 


§253]  AFFINITY.  461 

narrower  and  more  definite  term,  should  not  be  abandoned  in 
favour  of  the  latter,  or  some  other  similar  expression.  The 
study  of  affinity  would  then  be  advanced  by  all  the  methods 
which  are  available  for  studying  the  general  conditions  of 
chemical  equilibrium.  These  methods,  as  we  found  in  pars. 
185  et  seq.,  are  broadly  divisible  into  two  groups,  thermo- 
dynamical  and  molecular. 

Researches  such  as  those  of  Horstmann,  and  Gibbs,  must 
largely  advance  our  knowledge  of  affinity,  considered  from 
the  thermodynamical  point  of  view,  while  such  investigations 
as  those  of  Wright,  and  Helmholtz,  must  do  much  to 
elucidate  this  subject  when  regarded  from  the  molecular 
stand-point. 

The  theory  of  Guldberg  and  Waage,  and  its  development 
and  application  by  Ostwald,  will  remain,  as  the  great  advance 
made  in  recent  times  in  what  may  be  called  the  practical 
aspects  of  the  subject  of  affinity. 


CHAPTER   IV. 

OTHER    APPLICATIONS    OF    KINETICAL  METHODS. 

254.  I  HAVE  frequently  referred  to  the  need  of  keeping 
distinct  the  consideration  of  molecular  phenomena  occurring 
in  gases,  from  that  of  analogous  phenomena  occurring  in  solid 
or  liquid  substances.  Even  in  the  former  cases,  many  occur- 
rences are  more  probably  to  be  regarded  as  connected  with  the 
actions  and  reactions  of  groups,  or  aggregates,  of  molecules, 
than  with  mutual  actions  between  the  individual  molecules 
themselves. 

A  full  consideration  of  this  subject  would  lead  us  into 
the  domain  of  pure  physics;  there  are  however  some  points 
which  suggest  important  chemical  questions. 

In  examining  the  phenomena  of  isomerism,  we  found  that 
the  formula  chosen  to  represent  this  or  that  compound,  is 
sometimes  selected  from  among  several  possible  formulae, 
by  considering  certain  physical  constants  of  the  compound 
when  in  the  liquid  (or  even  solid)  state.  In  such  a  case  the 
assumption  is  made,  that  some  of  the  physical  properties  of 
the  compound  in  question  are  connected  with  the  relative 
arrangement  of  the  atoms  in  the  molecule  of  this  compound. 
The  fact  that  the  compound  can  be  gasified  and  again 
condensed  without  any  change  of  properties  renders  this 
assumption  very  probable.  In  any  case,  however,  the  term 
molecule,  as  here  employed,  means, '  that  small  part  of  the  gas', 
obtained  by  heating  the  liquid  compound,  'the  parts  of  which 
do  not  part  company  during  the  motion  of  agitation  of 
that  gas.'  But  there  are  other  physical  properties  which  are 
more  usually  regarded  as  depending  on  the  nature  of  those 


§  254]  APPLICATIONS    OF    KINETICAL    METHODS.  463 

groups  of  molecules,  the  parts  of  which  do  not  part  company 
during  such  processes  as  diffusion,  rise  of  temperature  not 
involving  change  of  state  from  liquid  to  gas,  &c.  Or,  it  may 
be,  that  the  same  physical  property,  e.g.  power  of  rotating 
the  plane  of  polarisation  of  a  ray  of  light,  is  sometimes  to  be 
associated  with  the  structure  of  the  molecules  of  a  compound, 
and  in  other  cases  with  the  nature  of  the  molecular  aggre- 
gates which  probably  form  the  reacting  units  of  the  same 
compound  when  in  the  liquid  state. 

The  molecular  weights  and  the  chemical  properties  of 
certain  gaseous  compounds  may  be  known,  and  the  chemical 
properties  of  the  liquids  obtained  by  condensing  these  gases 
may  also  be  known,  and  yet  it  may  not  be  possible  to  say 
how  far  the  latter  properties  are  to  be  regarded  as  correlated 
with  the  mutual  relations  of  the  atoms  constituting  the  gas- 
eous molecules  of  the  compounds  in  question,  rather  than 
with  the  mutual  relations  of  the  molecules  which  probably 
compose  the  reacting  units  of  the  same  compounds  when  in 
the  liquid  state.  In  other  words,  it  is  often  difficult  to  decide 
whether  a  definite  chemically  homogeneous  gas  is,  or  is  not, 
to  be  regarded  as  chemically  identical  with  the  compound 
obtained  by  condensing  that  gas  to  the  liquid  form. 

The  existence  of  the  gases  S6  and  S2,  O3  and  O2,  N2O4  and 
NO2,  Sn2Cl4  and  SnCl2,  Fe2Cl4  and  FeCl2,  &c.,  warns  us 
against  asserting  that  all  the  chemical  properties  of  a  gas, — 
that  is,  on  the  present  view,  the  properties  dependent  on 
the  mutual  relations  between  the  atoms  which  form  the 
molecules  of  the  gas, — are  the  same  as  the  chemical  properties 
of  the  liquid  which  is  obtained  by  condensing  that  gas. 

All  precise  conclusions  regarding  the  valencies  of  atoms 
and  the  distributions  of  atomic  interactions  (so  far  as  such 
conclusions  can  be  precise)  must  be  applied  only  to  gaseous 
compounds.  Nevertheless,  as  the  chemical  relations  between 
compounds  are  more  frequently  determined  from  the  study  of 
liquid,  than  of  gaseous  substances,  we  are  obliged,  granting 
the  theory  of  valency,  to  regard  these  relations  as  to  a  great 
extent  conditioned  by  those  between  the  atoms  which  consti- 
tute the  true  molecules  of  the  compounds  in  question.  When 


464  CHEMICAL  KINETICS.  [§  254 

however  we  do  not  know  the  molecular  weights  of  compounds 
in  the  state  of  gas,  conclusions  regarding  the  structure  of 
the  molecules  of  these  compounds  are  very  apt  to  degenerate 
into  mere  exercises  of  fancy.  Indeed  the  use  of  the  expres- 
sion '  structure  of  molecules '  is  in  such  cases  quite  unwar- 
ranted1. 

More  than  one  compound  may  be  produced  by  the  group- 
ing together  in  various  ways  of  the  same  molecules,  or  by 
variations  in  the  numbers  of  the  molecules  which  form  the 
reacting  unit  of  each  compound.  If  certain  compounds  are 
capable  of  existing  as  gases,  and  if  it  is  assumed  that  the 
relative  weights  of  the  true  molecules  of  these  compounds  are 
known,  still  it  does  not  follow  that  the  properties  of  the  react- 
ing units  of  the  actually  occurring  compounds  are  the  sums 
of  the  properties  of  the  molecules  which  form  these  units. 
As  the  properties  of  a  molecule  are  not  the  sum  of  the  pro- 
perties which  characterise  the  separated  atoms  of  that  mole- 
cule, so  the  properties  of  an  aggregate  of  molecules  may  not 
be  the  sum  of  the  properties  of  the  separated  molecules ;  but 

1  Could  there  be  a  rough  classification  of  chemical  compounds  founded  on 
these  considerations  ? 

(1)  Compounds,  the  properties  of  which  are  not  quite  the  mean  of  those  of 
their  constituents,  but  which  are  easily  separated  into  definite  constituents  ; 
e.  g.  sulphuryl  dibromide.     The  gases  evolved  by  heating  such  compounds 
are  only  mixtures,  the  compounds  are  not  re-formed  on  cooling  these  gases ; 
under  special  conditions,  chiefly  of  temperature  and  pressure,  the  gases  do 
combine,  but  the  combinations  are  very  unstable. 

(2)  Compounds  which  can  be  obtained  pure  only  with  much  difficulty,  if  at 
all ;  because  their  properties  are  connected  with  the  existence  of  groups  of 
molecules  (or  groups  of  atomic   aggregates),    the   composition   of  which 
groups  varies  within  certain  limits.     As  soon  as  attempts  are  made  to  re- 
move '  impurities,'  these  groups  become  unstable  and  undergo  rearrange- 
ment.    The  vapourisation  of  such  compounds  will  shew  distinct  analogies 
with  the  process  of  dissociation,  but  the  gas  obtained  will  probably  consist 
of  one  kind  of  molecules  only.     The  terpenes,  CnH2n_4,    may  possibly 
belong  to  this  group  of  compounds. 

(3)  Compounds  which  dissociate  on  being  heated  ;  the  gas  evolved  from  one 
of  these  compounds  is  a  mixture  of  atomic  aggregates,  which  recombine  on 
cooling,  to  produce  the  original  compound. 

(4)  Compounds  which  do  not  dissociate,  but  remain  unchanged,  when  in  the 
gaseous  state,  to  a  comparatively  high  temperature  whereat  true  decomposi- 
tion begins. 


§  255]          APPLICATIONS   OF    KINETICAL    METHODS. 

as  the  composition  of  such  an  aggregate  easily  undergoes 
change,  so  do  the  properties  of  the  compound  built  up  of  the 
aggregates  exhibit  variations1. 

No  kinetic  theory  of  liquids  and  solids  has  as  yet  been 
formed,  although  parts  of  such  a  theory  may  have  been 
sketched  in  outline 2. 

One  point  seems  clear,  namely,  that  the  explanation  of 
the  physical  properties  of  solids  and  liquids,  in  terms  of  any 
molecular  theory,  demands  the  existence  of  groups  of  mole- 
cules, which  behave,  under  certain  conditions,  as  individual 
systems,  but  separate  into  parts  more  readily  than  the  mole- 
cules of  gases. 

This  view  is  developed  in  Clerk  Maxwell's  article  on  the 
Constitution  of  Bodies*,  where  a  solid  is  regarded  as  a  body 
consisting  of  groups  of  molecules,  '  some  of  which  are  in 
different  circumstances  from  others/  Certain  of  these  groups 
may  break  up  by  the  effect  of  the  accumulation  of  the  ordi- 
nary agitation  of  the  molecules,  while  others  remain  unchanged 
'  unless  the  average  strain  exceeds  a  certain  limit/  The  latter, 
comparatively  stable  groups,  may  be  disseminated  so  abund- 
antly through  the  solid  as  to  form  a  kind  of  framework,  and 
thus  the  solid  as  a  whole  '  will  not  be  permanently  deformed 
except  by  a  stress  greater  than  a  certain  given  stress/ 

Now  chemical  phenomena  point  to  the  same  general  con- 
clusion as  that  obtained  by  physical  methods  of  enquiry. 

255.  If  then  it  is  so  difficult,  or  even  impossible,  to  apply 
the  molecular  theory,  in  its  kinetical  aspects,  to  the  chemical 
study  of  liquids  and  solids,  it  may  be  necessary  to  seek  for 
some  other  guide  in  this  study. 

It  would  obviously  be  absurd  to  have  recourse  to  the  con- 
ception of  equivalents  apart  from  the  light  thrown  thereon  by 
the  theory  of  atoms  and  molecules.  Perhaps  the  best  guide 
in  the  present  state  of  advance  is  the  periodic  law. 

We   are   again  brought  face  to  face  with   the   quest   so 

1  See  Lehmann's  classification  of  physical  isomerides,  ante,  book  I.  chap.  II. 
par.  94. 

2  See  Sir  W.  Thomson,  Nature,  30.  417. 

3  Rncyclopcedia,  Britannica  (pthed.). 

M.  C.  30 


466  CHEMICAL  KINETICS.  [§  256 

eagerly  followed  by  Dalton  and  Berzelius,  the  quest  for  the 
laws  of  atomic  synthesis. 

Is  it  possible  to  generalise  the  facts  regarding  the  combi- 
nations of  atoms  so  as  to  be  able  to  deduce  limiting  forms  for 
the  compounds  produced  by  the  union  of  any  given  elements  ? 
We  saw  in  a  former  chapter1  that  such  limiting  forms  may 
be  found  to  a  certain  extent,  without  employing  structural 
formulae,  or  indeed  committing  ourselves  to  any  theory  as  to 
the  connection  between  the  properties  of  compounds  and  the 
arrangements  of  the  particles  which  compose  them. 

The  symbols  which  express  the  forms  of  the  highest 
oxides,  or  other  salts,  characteristic  of  any  group  of  elements, 
do  not  profess  to  do  more  than  shew  the  ratio  of  the  numbers 
of  the  atoms  of  the  elements  in  the  reacting  units,  not  neces- 
sarily in  the  molecule,  of  the  oxide  or  other  salt.  When  the 
limiting  forms  have  been  established,  it  may  perhaps  be 
possible  to  shew  that  the  running  down  of  chemical  energy  to 
the  form  of  heat,  which  occurs  in  the  combinations  of  elements, 
is  connected  with  the  forms  of  the  salts  so  produced ;  and 
thus  to  establish  a  relation  between  the  limiting  forms  of  salts, 
and  the  limits  within  which  the  energies  of  the  systems  which 
produce  these  salts  can  undergo  degradation. 

256.  Before  a  structural  formula  can  be  assigned  to  a 
gaseous  compound,  or  to  a  liquid  the  molecular  weight  of  the 
gas  obtained  by  heating  which  is  known,  it  is  necessary,  as 
we  have  seen  again  and  again,  carefully  to  study  the  reactions 
of  the  compound  in  question.  The  formula  finally  given  to 
the  compound  interprets  the  results  of  this  study  in  terms  of  a 
special  theory  of  the  structure  of  matter. 

Now,  the  interpretation  of  a  number  of  chemical  changes, 
looked  at  from  the  point  of  view  of  one  of  the  changing  sub- 
stances, is  a  problem  essentially  belonging  to  chemical  kinetics. 
But  our  ordinary  structural  formulae  are  for  the  most  part 
founded  on  statical  considerations,  and  are  too  often  the  pro- 
ducts of  statical  methods  of  enquiry.  The  theory  of  chemical 
equilibrium  sketched  in  chapter  II.  of  this  book  (par.  187)  asso- 
ciates the  nature  of  a  process  of  chemical  change  which  any 

1  Book  i.  chap.  ill.  par.  114. 


§  256]         APPLICATIONS    OF    KINETICAL   METHODS.  467 

compound  can  undergo  with  the  affinities  of  the  constituents 
of  the  changing  system,  and  with  the  conditions  of  motion  of 
these  constituents.  But  the  conditions  of  motion  of  any  sub- 
stance depend,  not  only  on  the  motions  of  the  molecules  as 
wholes,  but  also  on  that  of  the  atoms,  or  groups  of  atoms, 
which  form  these  molecules,  and  on  the  ratio  of  these  two 
quantities. 

Moreover  this  ratio  may,  and  very  probably  does  vary  con- 
siderably, in  the  individual  molecules  of  any  one  constituent 
of  the  system.  But  any  structural  formula  assigned  to  a 
given  compound  represents  all  the  molecules  of  that  compound 
as  absolutely  identical  at  any  moment,  and  it  considers  these 
molecules  quite  apart  from  those  others  by  a  study  of  the 
mutual  actions  between  which  and  the  given  compound  the 
formula  professes  to  have  been  gained. 

From  a  consideration  of  the  work  of  Willard  Gibbs  on 
chemical  equilibrium  (see  par.  193  of  this  book),  taken  along 
with  Pfaundler's  hypothesis,  it  follows  (as  has  been  pointed  out 
on  p.  395),  that  chemically  heterogeneous  systems  apparently 
not  undergoing  chemical  change,  may  be  in  one  of  those 
phases  of  relative  instability  which  are  easily  overthrown  by 
contact  with  small  quantities  of  matter  in  other  phases.  This 
suggests  that  structural  formulae  may  sometimes  represent  the 
structure  of  molecules  only  when  they  are  in  certain  phases, 
which  are  stable  in  the  presence  of  matter  in  some  other, 
relatively  more  stable,  phase ;  or  that  the  phase  chosen  for 
representation  in  the  formula  may  be  one  which  is  very  easily 
overthrown  by  small  changes  in  the  surroundings  of  the  com- 
pound formulated1. 

The  possibility  of  one  compound  passing  through  several 
phases,  each  of  which  should  be  represented  by  a  different 
formula,  is,  it  is  true,  dimly  recognised  in  some  chemical  trea- 
tises ;  but  the  importance  of  this  almost  neglected  aspect  of 
formula-making  is  brought  prominently  forward  by  the  study 
of  chemical  change  and  chemical  equilibrium. 

1  The  examples  given  in  book  I.  chap.  II.  par.  77,  will  serve  to  illustrate  this 
suggestion.  See  also  the  account  of  the  reactions  of  the  alcohols  C4H9 .  OH  in 
Armstrong  and  Groves,  loc.  cit.  438 — 444. 

30—2 


468  CHEMICAL  KINETICS.  [§ 

It  would  be  very  difficult,  perhaps  impossible,  to  include 
much  information  regarding  the  methods  of  formation,  the 
relative  stabilities  under  different  conditions,  and  generally 
the  'power  of  doing'  of  a  compound,  in  a  single  intelligible 
and  not  too  cumbrous  formula.  I  call  the  student's  attention 
to  the  kinetical  aspects  of  the  structural  formulae  now  used  in 
chemistry,  because  I  consider  it  of  paramount  importance  that 
he  should  remember  how  little  information  these  formulae  give 
in  comparison  with  what  we  would  desire  to  have,  that  he 
should  not  forget  that  the  experimental  methods  by  which 
these  formulae  are  obtained  are  for  the  most  part  kinetical 
methods,  while  the  interpretation  of  the  results  is  expressed 
in  a  language  which  has  grown  out  of  almost  purely  statical 
considerations,  and  that  while  he  recognises  the  vast  import- 
ance of  structural  formulae,  he  may  still  refuse  to  bow  the  knee 
to  this  chemical  Baal,  which  has  been  set  up  in  these  times, 
so  aptly  described  by  Remsen  as  the  era  of '  formula  worship.' 
257.  Is  it  possible  to  connect  the  structure  of  the  mole- 
cules of  various  compounds,  as  this  structure  is  expressed  in 
formulae  based  for  the  most  part  on  statical  considerations, 
with  the  relative  affinities  of  these  compounds,  which,  as  we 
have  seen,  are  numbers  obtained  by  the  employment  of  kine- 
tical methods  of  research,  and  which  tell  a  great  deal  as  to 
the  power  of  doing  of  the  compounds  ? 

The  numbers  given  in  the  table  in  par.  235  (chap.  III.) 
represent  the  relative  affinities  of  a  series  of  acids,  including 
several  carbon  acids  the  structural  formulae  of  which  have 
been  well  established.  If  the  relative  affinities  of  the  chlor- 
acetic  acids  are  compared  with  that  of  acetic  acid,  and  if 
lactic  and  trichlorolactic  acids  are  also  compared,  we  have 
this  result. 

Acid.  Relative  affinity. 

Acetic  CH3-C02H  6-3 

Monochloracetic      CH2C1-CO2H  22 

Dichloracetic  CHC12-CO2H  52 

Trichloracetic  CC13-CO2H  87 

Lactic  CH3-CHOH-C02H  10-5 

Trichlorolactic  CC13  -  CHOH  -  CO2H  26 


§  257]          APPLICATIONS    OF    KINETICAL   METHODS.  469 

Substitution  of  Cl  for  H  in  acids  therefore  appears  to  be 
attended  by  an  increase  in  the  values  of  the  affinity-constants 
of  the  acids. 

The  substitution  of  OH  for  H  acts  in  a  similar  way.   Thus, 

Acid.  Relative  affinity. 

Isobutyric  (C3Hr)0.CO2H  5-8 

Hydroxyisobutyric    (C3H6  .  OH)0  .  CO2H  10 


Succinic  C2H4(CO2H)2  7 

Malic  C2H3(OH)(CO2H)2  n 

Tartaric  C2H2(OH)2(CO2H)2  15 

On  the  other  hand,  the  substitution  of  CH3  for  H  is  accom- 
panied by  a  decrease  in  the  values  of  the  affinity-constants  of 
the  acids  examined.  This  is  shewn  by  the  following  among 
other  numbers. 

Acid.  Relative  affinity. 
Formic          H.CO2H  12 

Acetic  CH3.CO2H  6.3 

Propionic      CH2  .  CH3  .  CO2H  5-5 

But  the  relative  affinities  of  methyl-,  ethyl-,  propyl-, 
and  amyl-sulphuric  acids,  viz.  100*4,  99*5,  99,  and  98, 
shew  that  the  substitution  of  CH3  for  H  in  the  molecule 
SO2.OH  .  OCnH2n+1,  is  attended  by  only  a  very  small 
decrease  of  affinity. 

Ostwald's  numbers  further  suggest  that  the  values  of  the 
affinity-constants  of  the  carbon  acids  are  conditioned  by  the 
relative  arrangements  of  the  atoms  in  the  molecules  of  these 
acids.  Thus,  comparing  the  relative  affinities  of  acetic  and 
trichloracetic  acids,  with  those  of  lactic  and  trichlorolactic 
acids,  we  see  that  the  difference  between  the  values  of  the 
quantities  in  question  is  much  larger  in  the  case  of  the  former 
than  of  the  latter  pair  of  acids.  Thus, 


Acid.  Relative  affinity.    Difference. 

807 


Acetic  CH3.CO2H  6-3 


Trichloracetic     CC13.  CO2H  87 

Lactic  CH3.CHOH.CO2H  10*5 

Trichlorolactic    CC13.  CHOH  .  CO2H  26 


47O  CHEMICAL   KINETICS.  [§  258 

The  replacement  of  H3  by  C13  is  accompanied  by  a  much 
greater  increase  of  affinity  when  there  is  direct  mutual  action 
between  the  C13  group  and  the  acid  group  CO2H,  than  when 
the  two  groups  are  separated  by  the  group  CHOH. 

The  influence  of  the  distribution  of  the  interatomic  actions 
on  the  affinity-constants  of  acids  is  also  illustrated  by  the 
following  numbers. 

Acid.  Relative  affinity. 

Oxalic  HO2C-CO2H  43 

H8 

Malonic  HO2C-C-CO2H  17-5 

Succinic  H O2C  -  C  -  C  -  CO2H  7 

Hn       Hn 


Lactic  CH3-CHOH-CO2H  10-5 

Methoxyacetic    CH2-OCH3-CO2H  13-5 

In  the  three  acids  oxalic,  malonic,  and  succinic,  we  notice 
a  rapid  decrease  in  the  value  of  the  affinity  as  the  mutual 
actions  of  the  carboxyl  groups  become  more  indirect;  and  the 
comparison  of  lactic  and  methoxyacetic  acids  suggests  that 
the  presence  of  the  group  H2C  —  OCH3  is  attended  with 
a  greater  affinity-value  than  that  of  the  isomeric  group 


258.  One  of  the  general  conclusions  regarding  the  rela- 
tions between  the  structure  of  carbon  compounds,  and  the 
refraction-equivalents  on  the  one  hand,  and  the  'specific 
volumes,'  (  F),  on  the  other,  of  these  compounds,  may  here  be 
recalled  (see  book  I.  chap.  IV.  pars.  141,  143,  and  154).  The 
refraction-equivalent,  and  also  the  value  of  (  V\  of  an  unsa- 
turated  compound,  i.e.  a  compound  in  the  molecule  of  which 
some  of  the  polyvalent  atoms  act  on  less  than  their  maximum 
number  of  monovalent  atoms  (see  book  I.  chap.  II.  par.  62), 
are  always  less  than  the  values  of  the  same  constants  for  an 
analogous  saturated  compound. 

Now  Briiril2  has  tried  to  shew  that  an  increase  of  the  refrac- 
tion-equivalent is  connected  with  a  loosening  of  the  attractions 

1  For  more  details  see  Ostwald,  J.  furprakt.  Chemie,  (2).  18.  362:  28.  479, 
488,  492:  29.  403. 

2  Ber.  14.  2533. 


§  258]          APPLICATIONS   OF   KINETIC AL   METHODS. 

between  the  atoms  in  the  molecules  of  compounds.  Briihl's 
reasoning  seems  to  me  to  be  very  unsatisfactory1.  But  a  similar 
conclusion  has  been  arrived  at  by  Schiff  from  his  measurements 
of  the  values  of  (  V)  for  a  large  series  of  compounds,  and  from 
some  general  considerations  drawn  from  the  kinetic  theory 
of  gases2.  Schiffs  comparison  of  (  V)  for  the  normal  acids 

C,.HM  C<°H,with(  F)forthe  normal  alcohols  CJi!mC^R, 

shews  that  the  value  of  ( V)  for  the  monovalent  oxygen  atom 
in  the  molecules  of  the  acids  increases  as  the  series  is  as- 
cended 3.  But,  if  we  admit  the  general  conclusion  arrived  at 
by  Briihl,  and  also  by  Schiff,  this  increase  is  accompanied  by 
an  increased  loosening  (Lockerung)  of  the  group  CO  .  OH. 
Such  a  loosening  would,  we  should  expect,  be  attended  by  a 
decrease  in  the  acidity  of  the  acids  of  the  series.  This  conclu- 
sion is  in  keeping  with  Ostwald's  values  for  the  relative 
affinities  of  the  three  acids,  formic,  acetic,  and  propionic,  viz. 
12,  6-3,  and  5-5. 

Whether  Schiffs  conclusion  is  accepted  or  not  must 
depend  upon  the  results  of  further  investigations.  There  is 
one  point  especially  worthy  of  note  in  the  nature  of  the  argu- 
ment adopted  by  Schiff,  namely,  it  is  based  on  measurements 
of  the  changes  in  the  values  of  ( V)  which  accompany  definite 
chemical  operations.  This,  it  seems  to  me,  is  as  it  should  be. 
As  we  require  determinations  of  the  changes  of  energy  which 
accompany  this  or  that  chemical  change,  so  we  must  have 
determinations  of  the  variations  in  such  physical  constants 
as  ( V\  (RA\  &c.,  which  proceed  along  with  definite,  and  if 
possible  simple,  chemical  processes. 

There  appears  to  be  a  definite  connection  between  the 
course  of  a  chemical  operation  and  the  ratio  of  the  original  to 
the  final  volume  of  the  reacting  system.  W.  Mtiller-Erzbach  has 
endeavoured  to  express  this  relation  in  the  so-called  '  law  of 
smallest  volumes,'  which  states,  that  the  smaller  the  volume 
occupied  by  the  products  of  a  chemical  change,  the  greater 

1  In  connection  with  this  see  Thomsen,  JBcr.  15.  67. 

2  Annalcn,  200.  321. 

3  For  data  see  Schiff,  loc.  cit.  314—315. 


4/2  CHEMICAL   KINETICS.  [§  259 

is  the  loss  of  energy  during  the  change,  and  therefore  the 
more  probably  will  the  change  occur1. 

^5>9-  *  Ostwald's  researches  suffice,  I  think,  to  establish  the 
e-justence.'of  a  connection  between  the  structures  and  the 
affinities  of  molecules.  In  other  words,  these  researches  put 
an  instrument  into  the  hands  of  chemists  by  the  use  of  which 
they  may  hope  to  gain  a  more  complete  answer  than  has 
hitherto  been  possible  to  some  of  the  questions  which  lie  at 
the  root  of  chemical  science.  A  structural  formula,  which  is 
the  result  of  an  extended  investigation,  summarises  a  great 
many  facts  about  the  composition,  and  also  tells  something  of 
the  reactions,  of  the  compound  formulated ;  the  number 
which  represents  the  relative  affinity  of  the  same  compound  is 
obtained  by  comparing  the  power  of  doing  of  the  substance 
with  that  of  other  substances,  and  enables  us,  to  some  extent, 
to  predict  the  course  and  the  results  of  the  chemical  changes 
that  will  occur  in  given  systems  of  which  the  substance  forms 
a  member. 

The  structural  formula  is  based  on  the  molecular  and 
atomic  theory,  and,  in  so  far  as  it  has  been  obtained  by 
assuming  the  theory  of  valency,  it  includes  in  its  expression 
the  older  views  regarding  equivalency.  It  may  be  possible, 
some  day,  to  indicate  by  this  formula  the  relative  loss  or  gain 
of  energy  which  has  occurred  in  the  passage  from  some 
standard  state  to  the  state  expressed  by  the  formula.  The 
relative  affinity,  on  the  other  hand,  is  based  on  a  kinetic 
theory  of  chemical  action,  and  is  the  outcome  of  the  study,  for 
three-quarters  of  a  century,  of  chemical  change.  We  begin  to 
see  how  the  formula  and  the  affinity  may  be  merged  into  a 
common  expression,  which  shall  tell  us,  not  only  the  compo- 
sition, but  also  the  function  of  the  substance,  and  in  doing  so 
will  reconcile  the  two  schools  which  have  so  long  existed  in 
chemistry,  the  school  of  Bergmann,  Berzelius,  and  Dalton, 
with  that  of  Berthollet,  Davy,  and  Dumas. 

1  Annalen,  218.  113.  See  also  Ber.  14.  217  and  2212;  16.  758:  17.  198. 
Also  Donath  and  Mayrhofer,  Ber.  16.  1588.  Compare  also  Spring's  work  on  the 
connection  between  allotropy  and  volume  ;  see  foot-note  on  p.  137. 


CONCLUDING   REMARKS. 


Concluding   Remarks. 

We  have  thus  tried  to  gain  some  answers  to  the 
with  which  we  started,  What  is  the  composition  of 
pounds  ?  What  actions  are  compounds  capable  of  per- 
forming ?  A  complete  answer  to  either  question  will  be  an 
answer  to  both,  and  that  answer  will  include  the  whole  of 
chemistry. 

The  atom  of  the  chemical  element  has  been  the  unit  with 
which  we  have  had  to  deal ;  the  properties  of  compounds  have 
been  regarded  as  conditioned  on  the  one  hand  by  the  nature, 
the  number,  and  the  arrangement  of  the  elementary  atoms 
which  together  form  the  compound  molecules,  and  on  the  other 
hand,  by  the  greater  or  smaller  quantities  of  energy  associated 
with  these  molecules.  To  determine  the  relations  between 
the  properties  of  various  molecules,  and  the  nature,  number, 
and  arrangement  of  their  constituent  atoms  was  the  first 
part  of  our  task ;  to  attempt  an  outline  of  a  dynamical  expla- 
nation of  chemical  operations  between  molecules  was  the 
object  of  the  second  part  of  the  undertaking. 

But  inasmuch  as  the  properties  which  chiefly  concern  us  as 
chemists,  are  the  properties,  not  of  individual  substances,  but 
rather  of  these  considered  as  members  of  changing  systems,  it 
has  been  impossible  to  consider  the  questions  arising  in  the 
first  part  without  to  a  great  extent  making  use  of  methods, 
and  conceptions,  more  strictly  belonging  to  the  second  part 
of  our  subject. 

The  facts  connoted  by  the  expression  chemical  statics  were 
.to  some  extent  classified  by  the.  help  of  the  hypothesis  of 
valency,  itself  an  outcome  of  the  application  of  the  molecular 
and  atomic  theory  to  chemical  phenomena,  and  by  the  hypo- 
thesis regarding  the  relations  between  the  atomic  weights  of 
the  elements,  and  the  properties  of  these  elements  and  their 
compounds,  which  is  known  as  the  periodic  law.  The  deter- 
mination of  physical  constants,  and  more  particularly  the 


474  CONCLUDING   REMARKS. 

quantities  of  heat  evolved  or  absorbed  during  chemical  changes, 
the  refraction-equivalents  and  specific  rotatory  powers,  and 
the  relative  volumes,  of  typical  compounds  and  classes  of 
compounds,  helped  somewhat  towards  a  definite  knowledge 
of  the  composition  of  these  compounds. 

The  study  of  chemical  kinetics  was,  we  found,  much  ad- 
vanced by  the  dynamical  hypothesis  of  Guldberg  and  Waage, 
which  in  its  primary  form  is  nearly  independent  of  any 
molecular  theory  of  the  structure  of  matter,  but  in  its  develop- 
ment and  application  by  Ostwald  forms  a  bridge  connecting 
the  investigation  of  the  chemical  properties  of  molecules  with 
that  of  the  actions  of  the  forces  which  come  into  play  during 
chemical  operations.  The  thermodynamical  methods  of  in- 
vestigation introduced  by  Horstmann,Gibbs  and  others,  and  the 
electrical  methods  founded  on  the  work  of  Joule  and  Thomson, 
and  developed  by  Helmholtz  and  Wright,  also  helped  us  to 
gain  some  conceptions  of  the  conditions  under  which  chemical 
changes  proceed,  and  chemical  equilibrium  is  established,  and 
at  the  same  time  threw  a  little  light  on  the  most  profound 
parts  of  chemical  phenomena,  the  nature  and  conditions  of 
action  of  the  forces  concerned  in  the  combinations  and  decom- 
positions of  the  elementary  atoms. 

I  have  tried  always  to  exhibit  the  hypotheses  of  chemistry 
as  at  once  arising  from  facts,  and  serving  as  guides  in  the 
quest  for  facts.  It  is  especially  necessary  to  do  this,  I  think, 
in  dealing  with  the  questions  concerning  structural  formulae. 
If  these  formulae  are  dissociated  from  the  chemical  facts  which 
they  symbolise  they  become  intellectual  tyrants ;  if  each 
formula  is  considered  simply  as  a  summary  of  facts  regarding 
the  compound  formulated,  they  are  to  be  classed  with  the 
other  '  brute  beasts  of  the  intellectual  domain,'  and  cease  to 
have  much  interest  for  one  who  believes  that  chemistry  is  a 
branch  of  science. 

One  great  difficulty  in  using  chemical  hypotheses  consists 
in  determining  the  limits  of  the  class  of  phenomena  to  which 
each  hypothesis  may  be  applied.  Berzelius  carried  the  hypo- 
thesis of  dualism  too  far,  and  it  was  destroyed  by  the  more 
elastic  hypothesis  of  substitution  ;  in  our  own  day  the  hypo- 


CONCLUDING   REMARKS.  475 

thesis  of  valency  has  frequently  been  applied  to  phenomena 
with  which  it  has  little  or  nothing  to  do. 

But  each  failure  to  explain  all  in  terms  of  one  hypothesis 
makes  us  more  hopeful  for  the  future,  and  convinces  us  that 
we  have  to  deal  with  a  living  and  growing  part  of  the  study 
of  nature. 

Much  work  has  yet  to  be  done  before  a  general  theory  of 
chemical  change  can  be  hoped  for ;  a  theory  which  shall 
represent  every  process  of  change  as  a  function  of  the  atomic 
weights  of  the  elements,  and  the  affinities  of  the  reacting 
substances  concerned  in  the  operation.  When  such  a  theory 
is  attained,  will  chemistry  be  complete  ?  I  hope  not ;  for 

'  What's  come  to  perfection  perishes.' 


INDEX. 


The  numbers  refer  to  pages. 


ABSORPTION-SPECTRA    and   molecular 

structure,  connection  between,  331 
Acetic  acid,  density  of  vapour  of,  205, 

363 

Acids,  action  of  metals  on,  92,  102,  270 
,,      affinities,  relative,  of,  417,  421, 

422 

,,      classification  of,  by  help  of  ther- 
mal data,  279 

,,      Davy's  and  Dulong's  views  re- 
garding, in 
„      electrolysis  of,  93 
,,      Lavoisier's  views  regarding,  in 
,,      Liebig's  views  regarding,  112 
Affinity,  a  unit  of,  use  of  expression  in 
theory  of  valency,  124,  126 
,,        attempts  to  measure,  in  terms 

of  electromotive  force,  453 
,,        Berthollet's  work  on,  403 
,,        Berzelius's  conception  of,  109, 

373 

,,  classification  of  methods  of  in- 
vestigating, 405 

,,        coefficients  of,  409,  449 

,,  connections  between,  and 
changes  of  energy,  443,  448 

,,  connections  between,  and  law 
of  maximum  work,  445,  note 

„  connections  between,  and  mole- 
cular structure,  468 

,,  constants,  specific,  general  re- 
marks on,  442 

,,  constants,  specific,  of  acids, 
429,  432 

,,        general  remarks  on,  458 

,,  is  it  connected  with  potential 
energy  of  atoms?  443,  445 

,,       predisposing,  376,  427 

,,  regarded  from  standpoint  of 
vortex  atom  theory,  450 

,,  researches  of  Ostwald  on,  416 
et  seq. 

,,        tables  of,  401 

,,  theory  of  Guldberg  and  Waage 
regarding,  407  et  seq. 


Affinity,  thermally  considered,  298,  433, 

443»  448 
,,        use  of  term  by  older  chemists, 

401 

Affinities,  relative,  of  acids,  417, 421, 422 
,,  ,,  ,,        tables        of, 

439'  441 

Alchemy,  the  conceptions  underlying,  2 
Allotropy,  136 

,,          experiments  by  Spring  bear- 
ing on,  137  note 

,,          thermally  considered,  273 
Antimony  group  of  haloid   salts   con- 
sidered thermally,  276 
Asymmetric  atoms  of  carbon,  323 
ATKINSON,   R.    W.,    his    experiments 
bearing  on  molecular  compounds,  220 
Atom,  Daltonian  definition  of,  8 

,,      definition  of,  obtained  by  apply- 
ing Avogadro's  law,  36 
,,      each,   has   a  definite    replacing 

!   value,  117 

,,      function  of  given,  dependent  on 

structure  of  molecule,  \ffiet  seq. 

, ,      of  oxygen  is  divalent,  meaning  of 

this  expression,  123  et  seq. 
,,      molecule,    and    equivalent,    the 

terms  contrasted,  24 
Atoms  and  molecules,    distinction   be- 
tween, based  on  reactions,  97 
,,      arrangement   of,   in    molecules, 

133  note,  149  note 
,,      double,  use  of  by  Berzelius,  19 
,,      equivalency  of  (see  also  valency>), 

116  et  seq. 

„      formula   for   finding    maximum 
number   of  monovalent,  in  a 
molecule,  139 
,,      valency   of    (see  also  valency), 

i2i,  131 
,,      valency    of,    in     non-gasifiable 

compounds,  132,  246,  463 
Atomic  heat  of  elements,  56,  64 

,,         ,,     of  oxygen  in  oxides,  234 
,,       refractions  of  elements,  316 


478 


INDEX. 


Atomic  synthesis,  Berzelian  rules  of,  17 

,,  ,,         Daltonian      ,,         10 

„  theory,  shortcomings  of  the 
Daltonian,  n 

,,  volumes  of  elements,  curve 
shewing,  226 

,,  weight,  of  an  element,  defini- 
tion of,  35 

,,       weights,  Berzelius's  table  of,  19 

„  ,,  data  required  before, 

can  be  determined, 
36 

„  ,,  determined  by  appli- 

cation of  Avogadro's 
law,  and  of  law  of 
Dulong  and  Petit,  64 

,,  ,,  determined  by  appli- 

cation of  Mitscher- 
lich's  law  of  isomor- 
phism, 69 

„  ,,  determined  .by  chemi- 

cal methods,  71 

,,  ,,  of  beryllium,  cerium 

metals,  and  uranium , 
determined  by  ap- 
plication of  periodic 
law,  233 

„  ,,  of  elements,  connec- 

tion between,  and 
heats  of  formation  of 
haloid  salts,  229 

,,  ,,  of  elements,  data  for, 

tables,  37,  78 

,,  ,,  of  elements,  periodic 

connection  between, 
and  properties  of 
elements,  223^  scq. 

,,  ,,         of  elements,  table  of, 

45 
Atomicity  of  molecules,  explanation  of 

term,  42 
,,  ,,  table  shewing, 

42 
Avidity,  meaning  of  term  as  used  by 

Thorn  sen,  437 

AVOGADRO,  application  of  his  law  to 
determine  atomic  weights, 
compared  with  applica- 
tion of  law  of  Dulong  and 
Petit,  64 
,,  his  distinction  between 

atom  and  molecule,  13 
,,  his  law,  13,  26 

,,  ,,         accepted  by  Du- 

mas, 20 

,,  ,,         applied  to  chem- 

ical reactions,  29 

,,  ,,         leads  to  definition 

of  atomic  weight, 
36" 


AVOGADRO,  his  law  made  basis  of  sys- 
tem of  Gerhard  t 
and  Laurent,  23 

,,  ,,         not    accepted    by 

Berzelius,  7 

BAKER,    H.,   his  work  in  connection 

with  isomoi-phism,  67  note 
Bases,  classification  of,  by  help  of  ther- 

mal data,  285 
BEMMELEN,  VAN,  his  experiments  bear- 

ing on  molecular  compounds,  217 
BERGMANN,  his  tables  of  affinity,  402 
,,  his    work    in    connection 

with  the  atomic  theory,  7 
BERTHELOT,  his  law  of  maximum  work, 

297,  445  note 

,  ,  his  thermal  investigation  of 

the  isomerides  benzene 
and  dipropargyl,  303 
,,  his  three  principles  of  ther- 

mal chemistry,  297 

BERTHOLLET,  his  study  of  affinity,  403 

,,  his      views      regarding 

chemical  change,  369 

,  ,  his  views  regarding  solu- 

tion, 370 

Beryllium,  atomic  weight  of,  233 
,,          fusibility  of  salts  of,  228 
,,          specific  heat  of,  58 
BERZELIUS,  his  acceptance  but  limita- 
tion of  Gay-Lussac's  law, 

17 

,,          his  conception  of  affinity, 

.373,458 
,  ,          his  electro-chemical  investi- 

gations, 1  08 
,,          his   rules   with    regard   to 

atomic  synthesis,  17 
,  ,          his  table  of  atomic  weights, 

J9 
,,          his  use  of  double  atoms, 


the  term  polarity, 


109 


,,  his  work  on  atomic  synthe- 

sis, 1  6 
,,          refuses  to  accept  Avogadro's 

law,  17 

.,          the  dualistic  theory  of,  ITO 

Boiling  points   of  carbon  compounds, 

connections  between,  and  structure, 

3°4 

Bonds,  free  and  satisfied,  129 
,,      relative  strength  of,  199 
,,      saturation  of,  128 
,,      Thomsen's   thermal    researches 

connected  with,  172,  300 
,,      use  of  term  in  theory  of  valency, 

1  24  et  seq. 


INDEX. 


479 


Boron,  carbon,  and  silicon,  Kopp's  hy- 
pothesis regarding  atoms  of, 63 
,,  specific  heat  of,  59  et  seq. 

BRAUNER,  his  investigations  connected 
with  the  periodic  law,  234,  237 

BRODIE,  his  work  bearing  on  structure 
of  small  particles  of  elements,  71 

Bromine,  density  of  gaseous,  209 

BRUHL,  his  work  on  the  refraction- 
equivalents  of  carbon  compounds,  309 
et  seq. 

BUNSEN  and  ROSCOE,  their  use  of  the 
term  induction,  378 

Calorimetric  equivalents,  meaning  of 
term,  290 

Calorimetric  equivalents  of  solutions, 
relations  between  and  composition, 
290 

CANNIZZARO,  his  generalisations  re- 
garding specific  heats  of  compounds, 

47.  55 

Carbon,  boron,  and  silicon,  Kopp's  hy- 
pothesis regarding  atoms  of, 

63 

,,       specific  heat  of,  59 
CARNELLEY,  his  determinations  of  fusi- 
bility of  elements,  228 
,,  his  papers  on  the  periodic 

law,  230  note,  248  note 
Catalytic  actions,  374,  430 
CAYLEY,  his  mathematical  examination 

ofisomerism,  \\Qnote 
Central  nucleus,  use  of  term,  165 
Cerium  metals,  atomic  weights  of,  236 
Chain,   dosed,   open,  side,  meanings  of 

terms,  163 
Chemical  and  electrical  forces,  relations 

between,  455 

Chemical  change,  Berthollet's  views  re- 
garding, 369 

,,  Berzelius's  views  re- 

garding, 109,  373 
,,  considered     thermo- 

dynamically  (Helm- 
holtz),  446 

,,  general       considera- 

tions regarding,  369 
,,  influence  of  mass  on, 

294,  381 

,,  influence  of  tempera- 

ture on,  391  note 
, ,  investigations  of  Har- 

court  and  Esson  on, 

399 

,,  physical  methods  of 

measuring,  417  note 

Chemical  changes  are  accompanied  by 
degradation  of  en- 
erg^  445  ™te,  446 


Chemical  changes  consist  of  two  parts, 

268,  296,  300 

,,  involving     degrada- 

tion of  energy  usu- 
ally    occur,     265, 
445  note 
Chemical  classification,  i,  116 

,,         equilibrium,    hypotheses    re- 
garding, 386  et  seq. 
,,         induction,    use    of   term    by 
Bunsen    and    Roscoe    (see 
also  induction)^  378 
„         methods      for       determining 
atomic    weights,    examples 
of,  71 

,,         methods  for  investigating  affi- 
nities of  the  acids,  424  et  seq. 
„         problems,  need  of  considering 
both  reacting  bodies    and 
forces  in,  5 

,,         Statics  and   Kinetics,  use  of 

these  terms  explained  and 

illustrated,  6,  353,  473 

Chemistry,  methods  by  which  brought 

under  domain  of  dynamics, 

5 

,,          thermal,  250  et  seq. 
, ,          the  fundamental  problem  of, 

4>  106,  373 

,,          the  general  scope  of,  i 
,,  the    sphere    of,    contrasted 

with  spheres  of  dynamics 

and  physics,  4 
,,          the  two  lines  of  advance  in, 

j,  116 
Chloral  hydrate,  density  of  vapour  of, 

365 
Chlorine,  density  of,  209 

,,         specific  heat  of,  51 
CLARKE,  F.  W.,  his  investigations  on 

hydrated  and  dehydrated  salts,  344 
Classification,  chemical,  based  on  theory 

of  types,  116 

, ,  of  acids  and  bases  by  help 

of  thermal  data,  279  et 
seq. 

,,  of    elements     and     com- 

pounds by  help  of  ther- 
mal data,  274 

,,  of  elements  in  accordance 

with  their  atomic  heats, 
56 

.,  of  elements  in  accordance 

with  the  periodic  law, 
224 

, ,  the  two  schemes  of,  adopt- 

ed in  chemistry,  i,  116 
Closed  chain,  meaning  of  term,  163 
Colloids     and    crystalloids,    216,    398 
note 


480 


LNDEX. 


Combining  weights  of  elements,  defini- 
tion of,  34 

„          weights  of  elements  do  not 
always  represent  equiva- 
lent weights,  1 6,  22 
Compound  radicles,  no,  114,  118 

,,  ,,         possess    a    definite 

replacing  power, 
117 

Compounds,  classification  of,  by  help  of 

thermal  data,  275  et  seq. 

,,  formulae   of    gaseous    and 

solid,  43,  132,  246 
,,  isomorphism  of,  65 

,,  molecular,  202  et  set/.,  398 

,,  specific  heats  of,  46,  55 

Constitution,  water  of,  343 
Contact-actions,  374,  430 
COOKE,  J.  P.,  his  experiments  in  con- 
nection with  physical  isomerism,  184 
COUPER,  his  work  bearing  on  valency 

of  atoms,  118 

CROSS,   on  the  action   of  carbon   and 
phosphorus  on  sulphuric  acid,  96  note 
Cryohydrates,  214,  397 
Crystalline  form,  determination  of,  as 
aid     in     fixing      atomic 
weights,  69 

„  salts,  dehydration   and   re- 

hydration    of,    210,    215, 
2i7>  343 

Crystallisation,  water  of,  210,  343 
Cumulative  resolution,  383 


DALE  (see  GLADSTONE) 

D ALTON,  development   of  the   atomic 

theory  of,  8 
„         his  New  System  of  Chemical 

Philosophy,  9 
, ,         his  reasons  for  giving  to  water 

the  formula  HO,  u 
,,         his   refusal    to    accept   Gay- 

Lussac's  law,  12 
,,         his  remarks  on  specific  heats 

of  solids,  liquids  and  gases, 

.45 
,,         his   rules   respecting   atomic 

synthesis,  10 
,,         shortcomings   of  his   atomic 

theory,  n 

DAVY,   his  electro-chemical   investiga- 
tions, 1 06 

,,       his  views  regarding  acids,  in 
DEBRAY,  his  work  on  dissociation,  357 
DEVILLE,  his  work  on  dissociation,  356 
„         his   work   on   the   action   of 

nitric  acid  on  metals,  94 
Dimorphism,  69 
Disgregation,  meaning  of  term,  444 


Dissociation,  analogies  between,    and 

evaporation,  356 

,,  bearing  of,  on  determina- 

tions  of  vapour-densi- 
ties, 362 
,,  general     phenomena    of, 

356  «f  seq. 

,,  of  salts  in  solution,  367 

,,  phenomena  more  or  less 

analogous  to,  366 
,,  special  characteristics  of, 

361 

,,  treatment  of,  by 

Debray,  357 
Deville,  356 
Gibbs,  396 
Hicks,  393 
Horstmann,  393 
Pfaundler,  360,  393 
,,  use  of  term,  355 

Dissociation-pressure,  meaning  of  term, 

356 

Divalent,  the  atom  of  oxygen  is,  mean- 
ing of  expression,  123  et  seq. 
„        the  atom  of  tin  is,  in  given 
molecule,  but  is  tetravalcni 
in  another  molecule,  126 
DIVERS,  his  experiments  on  the  action 

of  tin,  &c.,  on  nitric  acid,  103 
DONATH,  his  determination  of  the  spe- 
cific heat  of  uranium  oxide,  55 
Dualism,  opposed  by  Dumas,  113 

,,         opposed  to  Faraday's  electro- 
lytic laws,  112 
,,         system  of,  introduced  by  Ber- 

zelius,  no 

DULONG  and  PETIT,  their  law  regard- 
ing specific  heats  of  solid  elements, 
46,  63 
DUMAS,  his  early  acceptance  of  Avo- 

gadro's  law,  20 

,,        his  system  of  notation  partly 

atomic,  partly  equivalent,  20 

,,        introduces  the   conception   of 

types,  113  etseq. 

,,        opposes  the  dualistic  system  of 
Berzelius,  113 

Eka-aluminium,    eka-boron,    and    eka- 
silicon,  231 

Electro-chemical  investigations  of 
Berzelius,  108 
Davy,  106 
Faraday,  112,  451 
Helmholtz,  455 
Joule,  452 
Thomson,  453 
Wright,  454" 

Electrolysis  of  acids,  93 
,,  water,  100 


INDEX. 


481 


Element,  the  old  conception  of,  i,  248 

note 
Elements,  atomic  heats  of,  56 

,,  atomic  weights  of,  data  for 
finding,  tables,  37  et  seq., 
78  et  seq. 

,,         atomic  weights  of,  table,  45 
,,         atomic  volumes,  curve  of,  226 
,,         atoms   of,   have   definite  re- 
placing values,  117 
,,         atoms  of,  valency  of  (see  also 

valency  of  atoms),  121 
,,         classification  of,  by  help  of 

thermal  data,  274 
,,         classification   of,  in   accord- 
ance   with    their     atomic 
heats,  56 

,,  classification  of,  in  accord- 
ance with  the  periodic  law, 
224 

,,         fusibility  of,  228 
,,         isomorphism  of,  67 
,,         periodic  connection  between 
atomic   weights   and  pro- 
perties of,  223  el  seq. 
,,         specific  heats  of,  law  of  Du- 
long  and  Petit  regarding,46 
,,         specific  heats  of  some,  deter- 
mined indirectly,  51  et  seq. 
,,         specific  heats  of,  table,  48 
, ,         study  of  properties  of,  by  help 

of  the  periodic  law,  233 
,,         unknown,  properties  of,  pre- 
dicted by  the  periodic  law, 
230 
Elementary  gases,   table   of  molecular 

weights  of,  3  r 

Endothermic  and  exothermic  changes, 
meaning  and  application  of  terms, 
254,  446 

Energy-changes  accompanying  chemical 
changes,  1 75, 265, 406 
,,  connected  with  affinity- 

changes,  443,  448 
,,  measurements    of,     by 

electrical      methods, 

453 

,,  measurements     of,    by 

thermal  methods, 250, 
257,  288 

Energy,  degradation  of,  accompanying 
chemical  changes,  445  note, 
446 
,,       free  and  bound,  use  of  terms  by 

Helmholtz,  446 

Equilibrium,   chemical,  hypotheses  re- 
garding, 386  et  seq. 
,,  chemical,     equation      of 

(Guldberg  and  Waage), 
408 

M.  C. 


Equilibrium-pressure,   use   of  term    in 

connection  with  dissociation,  356 
Equivalency  of  atoms  (see  also  valency}, 

116  et  seq. 

,,  an,  use  of  term,  124 

Equivalent,  atom,  molecule,  the  terms 

contrasted,  24 
,,          connected    with    function, 

14,  22,  472 
, ,          difficulty  of  determining  the 

true,  of  an  element,  14 
, ,          notation,  inconveniences  of, 

J4  . 
,,          term  introduced   by   Wol- 

laston,  14 

,,          weights  of  elements  deter- 
mined by  Laurent,  22 
Equivalents,  work  of  Dumas,  Laurent, 

and  Gerhardt  on,  20 
,,  work  of  Ostwald  on,  com- 

pared with  earlier  investi- 
gations, 472 

ESSON  (see  HARCOURT) 
Etherification-values,     connection     be- 
tween, and  molecular 
structure   of   alco- 
hols, 351,  399 
,,  meaning  of  term,  348 

et  seq. 

,,  methods  of  determin- 

ing, 35° 

FARADAY,  his  electro-chemical  investi- 
gations, 112,  451,  455 
FISCHER,  his  work  in  connection  with 

the  atomic  theory,  7 
Fluorine,  specific  heat  of,  52 
Forms  of  oxides  and  salts  as  determined 
by  application  of  the  periodic  law,  243 
Formulae,  chemical,  of  gases  compared 
with   those   of  solids,  43, 
462 

„  chemical,  structural, examples 
of  methods  of  obtaining, 
144  et  seq. 

,,         chemical,  structural,  general-      /\ 
isations    usually   made    in 
obtaining,  151  et  seq. 
, ,         chemical,  structural,  regarded 
from     kinetical    point    of 
view,  466 

FRANKLAND  recognises  a  substituting 
value  for  each  elementary  atom,  117, 
122  note 

Fusibility  of  elements,  connection  be- 
tween, and  atomic  weights,  228 

Gallium,  identical  with  eka-aluminium, 

231 
GARNIER  and  CANNIZZARO,  their  gene- 

31 


482 


INDEX. 


ralisation  regarding  specific  heats  of 
compounds,  47,  55 
Gases,  formulae  of,  compared  with  those 

of  solids,  43,  462 
GAY-LUSSAC,  Berzelius  modifies  the  law 

of,  17 
,,  Dalton  refuses  to  accept 

the  law  of,  1 1 

,,  his    law   regarding  volu- 

metric combinations  of 
gases,  12 

GEOFFREY,  his  tables  of  affinity,  401 
GERHARDT,  his  law  of  even  numbers, 

76,  200 

,,  his   reasons   for    changing 

the  equivalents  of  carbon, 
&c.,  21 

GIBBS,  his  investigation  of  the  equili- 
brium of  heterogeneous  systems,  394 
et  seq. 

GLADSTONE,  his  investigations  on  chemi- 
cal change,  398 

GLADSTONE  and  DALE,  their  investiga- 
tions on  refraction-equivalents  of 
carbon-compounds,  307  et  seq. 
GLADSTONE  and  TRIBE,  their  investiga- 
tions in  connection  with  the  electro- 
lysis of  acids,  93 

GMELIN,  his  system  of  notation,  20 
GOLDSTEIN,  his  investigations  on  the 
connection  between  boiling  points  and 
molecular  structure,  305 
GRAHAM,  his  work   on   colloidal   and 
crystalloidal    matter,    216, 
398  note 

,,         his  work  on  water  of  crystal- 
lisation, 343 
GROTH,    his    investigations    regarding 

morphotropic  relations,  170 
Group,  use  of  term  in  nomenclature  of 

the  periodic  law,  224 
GULDBERG  and  WAAGE, 

their  theory  of  chemical  affinity,  407 

et  seq. 

their  theory  of  chemical  affinity  ap- 
plied by  Ostwald,  416  et  seq. 
their  theory  of  chemical  change,  373 
GUTHRIE,  his  work  on  cryohydrates, 
214 

Halogens,  hydracids  and  oxyacids  of, 
considered  thermally,  279 

HARCOURT  and  ESSON,  their  investiga- 
tion of  conditions  of  chemical  change, 

399 

HARTLEY,  his  investigation  of  relations 
of  molecular  structure  to  absorption- 
spectra,  331 

Heat,  connection  between  quantities  of, 
.  evolved  in  chemical  changes, 


and  structure  of  molecules   of 

changing  substances,  172  et  seq. 

Heat  evolved  in  chemical  changes,  study 

of,  250  et  seq. 
,,     evolved  in  reactions  of  isomerides, 

173  note,  175  et  seq. 
,,     of  formation  of  compounds,  mean- 
ing of  term,  260  et  seq. 
,,     of  neutralisation  of  an  acid  by  a 

base,  and  vice  versa,  279,  285 
(See    also    thermal    chemistry,    and 

thermal  data.) 

HELMHOLTZ,  his  electro-chemical  in- 
vestigations, 455 

,,  his  thermodynamical  con- 

siderations     regarding 
chemical  change,  446 
,,  his  use  of  the  terms  free 

and  bound  energy,  446 
HERMANN,  R.,  his  work  in  connection 

with  specific  heats,  47 
HICKS,  his  treatment   of  dissociation - 

phenomena,  393 

HOFF,  J.  H.  VAN'T,  his  hypothesis  re- 
garding optically  active  compounds, 
323  et  seq. 

HOOD,  his  experiments  on  the  influence 
of  temperature  on  the  rate  of  chemical 
change,  391  note 

HORSTMANN,  his  treatment  of  dissocia- 
tion-phenomena, 361,  393 
Hydration   and    dehydration   of    salts, 

210,  215,  217,  343 
Hydrofluoric  acid,  density  of  vapour  of, 

121  note 
Hydrogen,  replaceable,  illustrations  of, 

147,  158,  165,  169 
,,          specific  heat  of,  52 

latro-chemists,  2 

Induction,  chemical,    use   of  term   by 

Bunsen  and  Roscoe,  378 
,,          chemical,      regarded     from 
stand-point  of  equilibrium- 
theories,  398 

,,          chemical,   Wright's   experi- 
ments in  connection  with, 

378 
Iodine,  atomic  weight  of,  fixed  by  help 

of  periodic  law,  238 
,,      density  of  vapour  of,  208 
Isomerides,  formula  for  finding  maxi- 
mum number   of  monad 
atoms  in  molecules  of,  139 
,,          heat  evolved  or  absorbed  in 
reactions  of,  1 7  5  et  seq. ,  303 
Isomerism,    detailed   consideration   of, 

140  et  seq. 

„  exceptions      to       generally 

adopted  explanation  of,  1 8 1 


INDEX. 


4«3 


Isomerism,  hypothesis    by    which    ex- 
plained, 135 
,,  mathematical     examination 

of,  by  Cayley,  140  note 
,,  meaning  of  term,  134 

,,  thermally  considered,  172  et 

seq.,  302 

„  physical,  183 

,,  ,,         Lehmann's    work 

on,  185  et  seq. 
,,  study  of,  by  optical  methods, 

309  et  seq. 

,,  study  of,    by   thermal   me- 

thods, \1^etse 

Isomorphism  of  compounds,  65 
,,  of  elements,  67 

,,  Mitscherlich's  law  of,  65 

Isomorphous  crystals,  meaning   to   be 
given  to  this  expression,  67 

JOULE,  his  electro-chemical  investiga- 
tions, 452 

KAJANDER,  his  experiments  on  the  rate 

of  chemical  change,  400 
KANONNIKOW,  his  work  on  refraction- 
equivalents,  318  note 
KEKULE,  his  use  of  the  terms  atomic 
and  molecular  compounds, 
202 
, ,         his  work  on  valency  of  atoms, 

118 

Kinetics,  chemical,  general  remarks  re- 
garding, 353,473 

,,  ,,         use  of  term  explain- 

ed, 6 

KOPP,  his  hypothesis  regarding  the 
atoms  of  carbon,  boron,  and 
silicon,  63 

,,       his  investigations  regarding  spe- 
cific volumes,  335  et  seq. 
,,       his  investigations  regarding  spe- 
cific heats  of  elements,  fietseq. 

LAN  DOLT,  his  work  on  optical  activity 
of  carbon  compounds,  321 
et  seq. 

,,          his     work     on     refraction- 
equivalents,  307  et  seq. 
LAURENT,  his   definition   of  molecule 

and  atom,  23 
,,  his  system   based  on  Avo- 

gadro's  law,  23 

,,  his  work  on  equivalents,  21 

LAURIE,  A.  P.,  his  work  in  connection 
with  the  periodic 
law,  229 

LAVOISIER,  his  views  regarding  acids, 
1 06,  in 


Law,  Berthelot's,  of  maximum   work, 

297,  445  note 
,,      of  Avogadro  (see  also  AVOGAD- 

RO),  13,  26 

,,      of  Dulong  and  Petit,  46,  63 
,,      of  Gay-Lussac   (see  also   GAY- 

LUSSAC),  12 
,  ,      periodic  (see  also  periodic  law], 


LEHMANN,  his  work  on  molecular  com- 

pounds, 215 
,,          his  work  on  physical  isomer- 

ism,  185  et  seq. 

,,  his  work  on  the  hydration 
and  dehydration  of  salts, 
215 

LIEBIG,  his  views  regarding  acids,  1  12 
Links,  or  bonds,  use  of  term,  in  theory 

of  valency  (see  also  bonds),  124 
LOSSEN,  his  criticism  of  theory  of  bonds, 

124,  194^^. 
,,        illustrations   of  his   views  re- 

garding valency,  127 
,,        his  investigations   in   connec- 
tion with  specific  volume  of 
the  group  CH2,  339 

MALLET,  his  determination  of  the  den- 
sity of  the  vapour  of  hydro- 
fluoric acid,  121  note 
MARIGNAC,  his  work  on  the  supposed 

element  hyponiobium,  70 
Masses  of  reacting  substances,  influence 

of,  in  chemical  operations,  294,  381 
MAXWELL,  CLERK,  on  the  'constitution 

of  bodies  ',  465 

MENDELEJEFF,  his  researches  in  con- 
nection with  the  periodic  law,  230  et 
seq. 

MENSCHUTKIN'S  investigation  of  etheri- 
fication-values  of  alcohols  and  acids, 
348  et  seq.,  399 

Metals,  .action  of  acids  on,  92  et  seq.  102 
,,  action  of  acids  on,  considered 

thermally,  270 
Metamerism,  138 

MEYER,  L.,  his  calculation  of  the  spe- 

cific heat  of  beryllium,  59 

,  ,  his  work  in  connection  with 

the  periodic  law,  223  et 

seq. 

,,  his  work  in  connection  with 

specific  volumes,  346 
MEYER,    V.,   his   experiments   on  the 
vapour  density  of  fer- 
rous chloride,  75  note 
,,  his    experiments   on   the 

vapour  density  of  phos- 
phorus and  arsenic,  137 
note. 


484 


INDEX. 


MILLS,  on  cumulative  resolution,  383 
MITSCHERLICH,    his    law   of    isomor- 
phism, 65 

Molecular  compounds,  general  remarks 
on,  -202  et  seq., 
220,  398 

,,  ,,  Lehmann's  work 

on,  215 

,,  ,,  no  definition  of, 

possible,  203 

,,  groups,  existence  of,  in  gases, 
206 

,,  groups,  probable  existence 
of,  183  et  seq. 

,,  heat  of  solid  compounds, 
helps  to  determine  atomic 
weights  of  elements,  55 

,,  heat  of  solid  compounds, 
meaning  of  expression,  51 
note 

,,  phenomena  dealt  with  by 
statistical  methods,  91  note 

,,         structure,  133,  149  note,  385 

,,  structure,  connection  be» 
tween,  and  absorption- 
spectra,  331 

,,  structure,  connection  be- 
tween, and  affinity,  468 

,,  structure,  connection  be- 
tween, and  etherification- 
values,  351 

,,  structure,  connection  be- 
tween, and  optical  ac- 
tivity, 322  el  seq. 

,,  structure,  connection  be- 
tween, and  thermal 
changes,  172  et  seq. 

,,  structure,  connection  be- 
tween, and  various  con- 
stants, 170,  352  note 

,,  structure,  examples  of  de- 
pendence of  function  of 
part  of  a  molecule  on 
arrangement  of  all  the 
parts,  158  et  seq. 

,,  structure,  examples  of  pre- 
sence of  certain  atomic 
groups  in  molecules,  146 
et  seq. 

,,  structure,  further  examples 
of  (chiefly  physical),  170 
et  seq. 

,,  structure  of  solids  compared 
with  that  of  liquids  and 
gases,  462 

,,  theory,  general  sketch  of,  25 
et  seq. 

,,         weight  of  a  gas,  definition  of, 

3° 

,,         weight  of  a  gas,   examples 


shewing  how  determined, 

34 

Molecular  weight,  same  substance  may 
have  more  than  one,  33 

,,         weights  of  elementary  gases, 

table  of,  31 

Molecule,  atom,  equivalent,  the  terms 
contrasted,  24 

,,         physical  definition  of,  25 
Molecules   and  atoms,   distinction   be- 
tween,   based     on    reac- 
tions, 97  et  seq. 

,,  atomicity  of  elementary, 
table,  42 

,,  attempts  to  measure  ther- 
mal changes  accompany- 
ing separation  of,  into 
atoms,  269,  300 

,,  in    which    isomerism    may 

occur,  141 

,,  of  hydrogen,  &c.,  separate 
into  parts  during  chemical 
changes,  29 

,,  saturated  and  unsaturated, 
use  of  terms,  129 

,,  size  of,  27 

Monovalent  atoms,  formula  for  finding 
maximum  number  of,  in  a  molecule, 

J39 

Morphotropic  relations,  use  of  expres- 
sion by  Groth,  170 


Nascent  actions,  considered  from  kinet- 

fcal  stand-point,  391 

,,  ,,        considered   thermally, 

270  et  seq. 

,,  ,,        examples  of,  88 

,,  ,,        explanation  of,  given 

by     the     molecular 
theory,  89 

,,  ,,        general     remarks    on 

use   of  the   expres- 
sion, 105 
,,  „        Traube's   experiments 

on,  97  et  seq. 

,,       state  of  compounds,  90 
NASINI,  his   work   on   refraction-equi- 
valents, 314 

NAUMANN,    his  work   bearing  on   the 
subject  of  molecular  compounds,  204 
note,  208,  212 
NEUMANN,  his  extension  of  the  law  of 

Dulong  and  Petit,  46 
NEWLANDS,    his   work    in    connection 

with  the  periodic  law,  223 
NILSON  and  PETTERSSON,  their  deter- 
mination of  the  specific  heat  of  beryl- 
lium, 58 
NILSON  and  PETTERSSON,  their  work 


INDEX. 


485 


in  connection  with  the  periodic  law, 

334  et  seq. 
Nitrogen  group  of  oxides  and  oxyacids 

considered  thermally,  275 
Nitrogen,  specific  heat  of,  52 

,,          tetroxide,  density  of,  205* 
Nucleus,  central,  meaning  of  term,  165 

ODLING   introduces  notation    shewing 

valencies  of  elementary  atoms,  1 1 7 
Open  chain,  meaning  of  term,  163 
Optically  active   compounds,   meaning 

of  expression,  319 

Optically  active  compounds,  Van't 
Hoff's  hypothesis  concerning,  323  et 
seq, 

Optical   activity,   influence   of  inactive 

,,  „  solvents  on,  321,  329 

„  ,,        is    it    connected    with 

molecular  structure? 

327 
,,  ,,        of    solid    compounds, 

3*i,  330 
Optical  methods  applied  to   questions 

of  chemical  statics,  306  et  seq. 
Optical   methods   applied   to   study  of 

affinity,  422 
OSTWALD,  his  work  on  affinity,  416  et 

seq. 
Oxygen,    atomic   weight    of,    data    for 

determining,  36 

,,         in  oxides,  atomic  heat  of,  234 
,,  ,,          specific  heat  of,  54 

,,         specific  heat  of,  52 

PASTEUR,  his  supposition  regarding  the 

optical  activity  of  crystals,  330 
Periodic  law,  applied  to  predict  proper- 
parties  of  unknown  ele- 
ments, 230 

,,  applied  to  study  of  forms 

of  oxides  and  salts,  243, 
466 

,,  applied  to  study  of  pro- 

perties of  beryllium,  233 

,,  applied  to  study  of  pro- 

perties of  cerium  metals, 
236 

,,  applied  to  study  of  pro- 

perties of  uranium,  238 

,,  applied  to  study  of  pro- 

perties of  known  ele- 
ments, 233  et  seq. 

,,  applied  to  study  of  valen- 

cies of  elementary 
atoms,  245 

,,  classification    in    accord- 

ance with,  compared 
with  that  based  on 
thermal  data,  229,  774 


Periodic  law,  general  remarks  on,  247 
,,  illustrations  of,  226  et  seq. 

,,  nomenclature    employed, 

224,  230,  239 
,,  statement  of,  224 

,,  tables    shewing    arrange- 

ment of  elements  in 
accordance  with,  225, 
240 

Periods,  long,  short,  and  transition,  use 
of  terms  in  nomenclature  of  the 
periodic  law,  239 

PERK  IN,  on  the  connections  between 
molecular  structure  and  magnetic  ro- 
tation, 352  note 

PETIT  and  DULONG,  their  law  regard- 
ing specific  heats  of  solid  elements, 
46,63 

PETTERSSON  (see  NILSON) 
PFAUNDLER,  his  hypothesis  regarding 
chemical     equilibrium, 
387  ft  seq.  458 
,,  his  hypothesis  regarding 

dissociation,  360 

Phase,  use  of  expression  by  Gibbs,  395 
Phosphorus    group    of   oxyacids    con- 
sidered thermally,  281 
,,  pentachloride,    density   of 

vapour  of,  204,  364 

Physical  methods  applied  to  questions 

of  chemical  statics,  249  et  seq. 

,,        methods   applied   to  study  of 

affinity,  417  et  seq. 
,,        phenomena,          mathematical 

theories  of,  28 

PICKERING,  his  examination  of  the  ac- 
tion of  sulphuric  acid  on  copper,  94 
Polarity,  use  of  term  by  Berzelius,  109 
Polymerism,  138 
Polymorphism,  69 

POTILITZIN,  his  experiments  on  in- 
fluence of  mass  in  chemical  changes, 
295,  382 

Predisposing  affinity,  illustrations  of  use 
of  the  expression,  376 

Radicles,  compound,  114,  118 

,,  ,,  possess  a  definite 

replacing  power, 
117 
RAMSAY,  his  experiments  in  connection 

with  specific  volumes ',  337 
Refraction-equivalent  of  a   compound, 
is  it  equal  to  sum  of  equivalents  of 
elementary  constituents  ?  309  et  seq. 
Refraction-equivalent,  meaning  of  term, 

307 

Refraction-equivalents,  connection  be- 
tween and  structure  of  carbon  com- 
pounds, 310  et  seq. 


486 


INDEX. 


Refraction-equivalents,  connection  be- 
tween and  structure,  considered  kinet- 
ically,  470 

Refraction-equivalents,  formulae  for  de- 
termining, 307 

Refraction-equivalents    of    elementary 

atoms,  316 

,,  of    solid    com- 

pounds,   318 
note 

REGNAULT,  his  researches  on  specific 
heat,  47 

RICHTER,  his  work  in  connection  with 
the  atomic  theory,  7 

REYNOLDS,  R.  E.,  his  determinations 
of  the  specific  heat  of  beryllium,  58 

ROSCOE,  his  investigations  regarding 
the  atomic  weight  of  vanadium  (see 
also  BUNSEN),  71  note 

ROSE,  H.,  his  supposed  discovery  of  an 
allotropic  form  of  niobium,  70 

Rotatory  power,  specific,  determination 

of>321 

„  specific,  meaning  of  ex- 

pression, 320 

Salts,    hydration   and    dehydration   of, 

210,  215,  217,  343 
Saturated   and   unsaturated  molecules, 

use  of  terms,  129 
Scandium,    identical    with   Eka-boron, 

231 
SCHIFF,  his  work  in  connection   with 

specific  volumes,  336 
Series,  use  of  term  in  nomenclature  of 

the  periodic  law,  2-24 
Side  chain,  meaning  of  term,  165 
Silicon,    carbon,    and    boron,    Kopp's 
hypothesis  regarding  atoms 
of,  63 

,,         specific  heat  of,  59 
Solution,  Berthollet's  views  regarding, 

370 

Specific  affinity-constants  of  acids  and 

bases,  429,  432,  442 
Specific  heat  of  beryllium,  58 

,,         ,,         boron,     carbon,      and 

silicon,  59 

,,         ,,         oxygen  in  oxides,  54 
Specific  heats  of  compounds,  generali- 
sation of  Neumann 
regarding,  46 

,,  ,,  compounds,  generali- 
sation of  Garnierkand 
Cannizzaro  regard- 
ing, 47 

,,  ,,  elements,  law  of  Du- 
long  and  Petit  re- 
garding, 46,  63 


Specific  heats  of  some  elements   deter- 
mined indirectly,  51  et  seq. 
Specific  refractive  energy,  meaning  of 

expression,  307 
,,        rotatory  power,  determination 

of,  321 
,,        rotatory    power,   meaning    of 

expression,  320 
,,        imipolarity ,  use  of  expression 

by  Berzelius,  109 

,,  volume  of  a  compound  proba- 
bly equal  to  sum  of  volumes 
of  elementary  constituents, 

335.  34i,  345 

,,         volume  of  carbon  and  of  oxy- 
gen varies  according  to  the 
valency  of  the  atom  of  each 
element,  336  et  seq. 
,,        volume,  meanings,   of  expres- 
sion, 334,  417  note 
,,        volumes  of  atoms  in  molecules 
vary  according  to  distribu- 
tion   of    interatomic    reac- 
tions, 338 

,,        volumes   of  compounds,  con- 
sidered kinetically,  470 
,,        volumes  of  hydrated  and  de- 
hydrated salts,  343 
,,        volumes  of  solid  compounds, 

.342 
SPRING,  his  experiments  in  connection 

with  allotropy,  137  note 
Stability,  meaning  of  term  as  used  by 
Ostwald   in    his  work    on 
affinity,  426 
,,          vagueness  of  the  term,    179, 

383  note 
Stable    phases,    use   of  expression    by 

Gibbs,  395 
STVEDEL,   his    experiments   on   specific 

•volumes  of  carbon  compounds,  340 
Statics,  chemical,  questions  of,  studied 

by  physical  methods,  249 
,,       chemical,  use  of  expression,  ex- 
plained   and    illustrated,    6, 
353»  473 


Tables  of  affinity,  401,  402 

Table,  atomic  heat  of  oxygen  in  oxides, 

235 

,,       atomic  weights  of  elements,  45 
, ,       atomic  weights  of  elements,  data, 

37,  7.8 

,,  atomicity  of  elementary  mole- 
cules, 42 

,,  data  for  finding  maximum  atomic 
weight  of  oxygen,  36 

,,  densities  of  acetic  acid,  halogens, 
nitrogen  tetroxide  and  phos- 


INDEX. 


487 


phorus     pentachloride,     204, 
205,  208,  209 
Table,  molecular  weights  of  elementary 

gases,  31 
,,       relative   affinities   of  the   acids, 

439'  44i 
,,       periodic    arrangement    of     ele- 

ments, 225,  240 

,,       specific  heats  of  elements,  48 
,,       thermo-atomic     weights     (Reg- 

mult),  47 
Tellurium,  atomic  weight  of,  fixed  by 

application  of  the  periodic  law,  238 
Tetravalent,    the   atom    of   carbon    is, 

meaning  of  expression,  127 
Thermal  chemistry,  attempts  made  in, 
to  distinguish  between  the 
two    parts    of    a    chemical 
change,  268,  296,  300 
,,        chemistry,    Berth  clot's     three 

principles  of,  297 

,,        chemistry,  illustrations  of  me- 
thods of  calculation  used  in, 


chemistry,  need  of  considering 

action  of  excess  of  reacting 

substances  in,  294 
chemistry,  need  of  considering 

physical  conditions  of  chang- 

ing systems  in,  288,  293 
chemistry,   notation    used   in, 

251  efseq. 
chemistry,  principles  on  which 

based,  257 
chemistry,   the  law  of  maxi- 

mum work  in,  297  et  seq., 

445  note 
data,  applied  to  action  of  acids 

on  metals,  270  et  seq. 
data,  applied  to  action  of  anti- 

mony pentachloride  as  chlo- 

rinating agent,  268 
data,  applied  to  action  of  con- 

centrated and  dilute  hydri- 

odic  acid,  265 
data,  applied  to  action  of  sul- 

phuretted hydrogen  on  me- 

tallic salts,  266  et  seq. 
data,  applied  to  allotropy,  273 
data,  applied  to  classification 

of  acids  and  bases,  279  et 

seq. 
data,  applied  to  classification 

of  compounds,  2/5  et  seq. 
data,  applied  to  classification 

of  elements,  274 
data,  applied  to  study  of  affin- 

ity, 298,  433,  443,  448 
data,  applied  to  study  of  iso- 

merism,  172  et  seq.,  302 


Thermal  data,  examples  of  attempts  to 

analyse,  293 
,,        data,  influence  of  temperature 

on,  287 
,,        methods    used    in   chemistry, 

250 

THOMSEN,  J.,  his  attempt  to  measure 
heat  of  dissociation  oj 
the  carbon  atom,  269, 
300 

,,  his  attempt  to  measure 

the  thermal  value  of 
each  bond  of  the  car- 
bon atom,  1 74 

„  his  classification  of  acids 

and   bases,    based   on 
thermal  data,  2 "jgetseq. 
,,  his   examination   of  the 

relations  between  the 
calorimetric  equiva- 
lents and  the  compo- 
sition of  various  solu- 
tions, 289  et  seq. 

„  his  experiments  on  the 

connections  between 
thermal  changes  and 
molecular  structure, 
172  et  seq. 

,,  his  thermal  study  of  the 

affinities  of  acids,  433 
„  his  statement  of  the  law 

of  maximum  work,  299 
,,  his  use  of  the  term  avi- 

dity, 437 

THOMSON,  J.  J.,  his  study  of  affinity 
from  the  stand-point  of  the  theory  of 
vortex  atoms,  450 
THOMSON,  SIR  W.,  his  electro-chemical 

investigations,  453 

THORPE,  his  investigations  in  connec- 
tion with  specific  volumes, 
339  et  seq. 

,,        his  investigations   of  the  re- 
ducing action  of  metals  on 
ferric  sulphate,  96 
,,        and  WATTS,  their  experiments 
in  connection  with  water  of 
crystallisation,  343 
TOMMASI,  his  work  in  connection  with 

nascent  actions,  97 

TRAUBE,  his  experiments  in  connection 
with  nascent  actions,  97  et  seq.,  102 
et  seq. 

TRIBE  (see  GLADSTONE) 
Trimorphism,  69 

Types,   classification  based  on,  116 
,,       conception    of,   introduced    by 

Dumas,  113  et  seq. 

Typical  elements,  use  of  expression  in 
nomenclature  of  the  periodic  law,  241 


488 


INDEX. 


Uranium,  atomic  weight  of,    fixed  by 
application  of  the  periodic 
law,  238 
,,         specific  heat  of,  55 

Valency,  a,  use  of  expression,  124,  126 
Valency  of  atoms,  conception  of,  applied 

to  explain  molecular 

structure,  191  et  seq. 
„  conception  of,  applied 

to  finding  best  struc- 

tural  formula    for   a 

given  compound,  1  5  1 

et  scq. 
,,  data   for   determining, 

I2t,  131 
9>  discussion  of  notation 

adopted  in  theory  of, 

124  et  seq. 
,,  in  non-gasifiable  com- 

pounds, 132,246,  463 
,,  limitations  necessary  in 

applying  the  concep- 

tion of,  1  50 
,,  Lossen's  views  regard- 

ing,   124  et  seq.,  194 

et  seq. 
,,  meaning  of  expression, 

122 

„  probably  varies  period- 

ically   with    relative 
weights  of  the  atoms, 


,,  theory  of,  as  a  guide  to 

classifying  molecules, 
180 

Vapour  densities,  bearings  of  dissocia- 
tion   on    determina- 
tions of,  362  et  seq. 
„  definition  of  expression, 

32  note 
,,  methods  of  determining, 

34  note 

,,  must  be  supplemented 

-  by    analyses     before 

molecular  weights  of 

compounds    can     be 

found  by  means  of,  34 

Velocities  of  chemical  actions,  connec- 

tion between,  and  affinities  of  reacting 

substances,  410,  427,  430 

Volume,  atomic,  of  elements,curve  of,226 

,,        specific,    meaning   of    expres- 

sion, 334 


Volumetric  methods  of  studying  chemi- 
cal operations,  adopted  by  Ostwald, 
418 
Vortex  atoms,  bearing  of  theory  of,  on 

affinity,  450 

WAAGE  (see  GULDBERG) 
WARDER,  his  experiments  on  the  in- 
fluence of  temperature  on  the  rate  of 
chemical  change,  391  note 
Water,  basic  and  saline,  343 
,,        electrolysis  of,  100 
,,        of  constitution,  343 
,,        of  crystallisation,  210,  343 
WATTS  (see  THORPE) 
WEBER,  his  determinations  of  the  specific 
heats  of  boron,  carbon  and  silicon,  60 
WIEDEMANN,  E.,  his  attempt  to  mea- 
sure heat  absorbed 
in  separating  mole- 
cule   of    hydrogen 
into  atoms,  269 

,,  his  work   on   calori- 

metric   equivalents 
of  solutions,  291 

„  his  work   on   refrac- 

tion -  equivalents, 

307»  3*5 

WILLIAMSON,  his  hypothesis  regarding 
chemical    equilibrium, 
.387 
,,  his     researches     on    the 

ethers,  73 
WILLS,  his  determination  of  the  atomic 

weight  of  iodine,  238 
WITT,  his  experiments  on  the  connec- 
tion between  molecular  structure  and 
tinctorial  properties,  1 70 
WOLLASTON,  introduces  the  use  of  the 

term  equivalent,  14 
„  objections  to  his  method 

of  determining  equiva- 
lents, 14 
WRIGHT,  his  experiments  on  chemical 

affinity,  453 
„         his  experiments  on  chemical 

induction,  378 

WURTZ,  his  work  in  connection  with 
dissociation,  356,  364 


ZANDER,  his  experiments  on  specific 
volumes  of  carbon  compounds,  338 

ZIMMERMANN,  his  determination  of  the 
specific  heat  of  uranium,  55 


CAMBRIDGE:  PRINTED  BY  c.  j.  CLAY,  M.A.,  AND  SON  AT  THE  UNIVERSITY  PRESS. 


r WI/A.    C-- 


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UNIVERSITY  OF  CALIFORNIA  IvIBRARY 


